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Worksheet for Class 10 Mathematics Chapter 13 Surface Area and Volume
Class 10 Mathematics students should refer to the following printable worksheet in Pdf for Chapter 13 Surface Area and Volume in Class 10. This test paper with questions and answers for Class 10 will be very useful for exams and help you to score good marks
Class 10 Mathematics Worksheet for Chapter 13 Surface Area and Volume
Q.- A circus tent is in the shape of a cylinder, upto a height of 8 m, surmounted by a cone of the same radius 28 m. If the total height of the tent is 13 m, find:
MCQ
1. A Surahi is the combination of
(a) a sphere and a hemisphere
(b) a sphere and a cylinder
(c) two hemisphere
(d) a hemisphere and cylinder
2. A shuttle cock used for playing badminton has the shape of the combination of
(a) a cylinder and a sphere
(b) a sphere and a cone
(c) a cylinder and a hemisphere
(d) frustum of cone and hemisphere
3. A solid piece of iron in the form of a cuboid of dimensions 49 cm x 33 cm x 24 cm is melted to farm a solid sphere. The radius of the sphere is
(a) 21 cm
(b) 23 cm
(c) 25 cm
(d) 19 cm
4. If two solid hemisphere of same base radius r are joined together along their bases, then surface area of this new solid is
(a) 4πr2
(b) 6πr2
(c) 3πr2
(d) 8πr2
5. Twelve solid spheres of the same size arc made by melting a solid metallic cylinder of base diameter 2 cm and height 16 cm. The diameter of each sphere is
(a) 4 cm
(b) 3 cm
(c) 2 cm
(d) 6 cm
6. A hollow cube of internal edge 22 cm is filled with spherical marbles of diameter 0.5 cm and it is assumed that 81 space of the cube remains unfilled. Then the no. of marbles that the cube can accommodate is
(a) 142296
(b) 142396
(c) 142496
(d) 142596
7. A mason construction a wall dimensions 270 cm x 300 cm x 350 cm with the bricks each of size 22.5 cm x 11.25 cm x 8.75 cm and it is assumed that 1/8 space is covered by the mortar. Then the number of bricks used to construct the wall is
(a) 11100
(b) 11200
(c) 11000
(d) 11300
8. The radii of the top and bottom of a bucket of slant height 45 cm and 28 cm and 7cm respectively, the carved surface area of the bucket is
(a) 4950 cm2
(b) 4951 cm2
(c) 4952 cm2
(d) 4953 cm2
9. Volumes of two sphere are in the ratio 64 : 27. The ratio of their surface areas is
(a) 3 : 4
(b) 4 : 3
(c) 9 : 16
(d) 16 : 9
10. A right circular cylinder of radius r cm and the height h cm (h > 2r) just enclose a sphere of diameter
(a) r cm
(b) 2r cm
(c) h cm
(d) 2h cm
11. A medicine capsule is in the shape of a cylinder of diameter 0.5 cm with two hemisphere stack to each of its ends. The length of entire capsule is 2 cm. The capacity of the capsule is
(a) 0.36 cm3
(b) 0.35 cm3
(c) 0.34 cm3
(d) 0.33 cm3
12. The radii of the ends of a frustum of a cone 40 cm high are 20 cm and 11 cm. Its slant height is
(a) 41 cm
(b) 20√5 cm
(c) 49 cm
(d) √521 cm
13. A sphere of radius 6 cm is dropped into a cylindrical vessel party filled with water the radius of the vessel is 8 cm. If the sphere is submerged completely, then the surface of the water rises by
(a) 4.5 cm
(b) 4 cm
(c) 3 cm
(d) 2 cm
14. A solid consists of a circular cylinder with an exact fitting right circular cone placed at the top. If the height of the cone is h and the total volume of the solid is 3 times the volume of the cone, then the height of the circular cylinder is
(a) 2h
(b) 2h/3
(c) 3h/2
(d) 4h
SHORT TYPE QUESTIONS (2 marks each)
1. A cone of height 24 cm and radius of base 6 cm is made up of modelling clay, find the volume of cone.
2. The cylindrical cans have equal base areas. If one of the can is 15 cm high & other is 20 cm high, find the ratio of their volumes.
3. In a box whose dimensions are 12 cm x 4 cm x 3 cm, what is the length of the longest stick that can be placed ?
4. Find the volume of a cylinder whose height is 12 cm & radius is 5 cm.
5. It costs Rs.2200 to paint the inner curued surface of a cylindrical vessel 10 m deep. If the cost of painting is at the rate of Rs.20 per m2, find inner curved surface are of the vessel.
6. The height of a right circular cone is 12 cm & the radius of its base is 4.5 cm. Find the slant height.
7. A conical military tent having the diameter of the base is 24 m and slant height of the tent is 13 m, find the curved surface area of the cone.
8. A jokers cap is in the form of a right circular cone of base radius 7 cm & the slant height is 25 cm. Find the area of the cap.
9. The radius of the sphere is 6 cm. Find the volume of sphere.
10. Find the radius of the sphere whose surface area is 154 cm2.
11. Two cubes have their volume in the ratio 1 : 64. What is the ratio of their surface areas ?
12. A sphere of maximum volume is cut out from a solid hemisphere of radius 7 cm. What is the ratio of the volume of the hemisphere to that of the cut out sphere.
13. If the areas of circular bases of a frustum of a cone are 4 cm2 & 9 cm2 respectively & the height of the frustum is 12 cm, then find the volume of the frustum (take π = 22/7)
14. The radii of the bases of a cylinder and a cone are in the ratio 3 : 5 & their heights are in the ratio 3 : 4. What is the ratio of their volumes ?
15. A cone & a sphere have equal radii and equal volume. What is the ratio of the diameter of the sphere to the height of the cone ?
16. Determine the ratio of the volume of a cube to that of a sphere which will exactly fit inside cube.
17. One iron solid is a cubiod of dimentions 30 cm x 30 cm x 42 cm. If is melted & cubes each of side 3 cm & moulded from it. Find the number of cubes formed.
18. A granary is in the shape of a cuboid of size 8 m x 6 m x 3 m. If a bag of grain occupies a space of 0.65 m3. How many bags can be stored in the granary ?
19. 2 cubes each of volume 64 cm3 are joined end to end. Find the surface area of the resulting cuboid.
20. A vessel is in the form of a hollow hemisphere mounted by a hollow cylinder. The diameter of the hemisphere is 14 cm & the total height of the vessel is 13 cm. Find the inner surface area of the vessel.
LONG TYPE QUESTIONS (4 marks each)
1. The diameter of internal & external surface of a hollow spherical shell are 6 cm & 10 cm respectively. If it is melted & recast into a solid cylinder of height 2(2/3)cm, find the diameter of the cylinder.
2. A solid metallic sphere of diameter 28 cm is melted & recast into a number of smaller cones, each of diameter 324 cm & height 3 cm. Find the number of cones so formed.
3. Solid spheres of diameter 6 cm are dropped into a cylindrical beaker containing some water & are fully submerged. If the diameter of the beaker is 18 cm and the water rises by 40 cm, find the number of solid spheres dropped in the water.
4. A toy is in the form of a cone mounted on a hemisphere of common base radius 7 cm. The total height of the toy is 31 cm, find the total surface area of the toy. (use π = 22/7)
5. A toy is in the shape of a right circular cylinder with a hemisphere on one end & a cone on the other. The radius & height of the cylindrical part are 5 cm & 13 cm respectively. The radii of the hemispherical and conical part are the same as that of the cylindrical part. Find the surface area of the toy if the total height of the toy is 30 cm.
6. 4 right circular cylindrical vessels each having diameter 21 cm & height 38 cm are full of ice cream. The ice cream is to be filled in cones of height 12 cm & diameter 7 cm having a hemispherical shape on the top. Find the total number of such cones which can be filled with ice cream.
7. A circus tent is cylindrical to a height of 3 m & conical above it. If its base radius is 52.5 m & slant height of the conical portion is 53 m, tind the area of the canvas needed to make the tent.
8. A hollow cone is cut by a plane parallel to the base & the upper portion is removed. If the curved surface of the remainder is 8/9th of the curved surface of the whole cone, find the ratio of the line segments into which the cones altitude is divided by the plane.
9. If the radii of the ends of a bucket, 45 cm high, are 28 cm & 7 cm. Find its capacity & surface area.
10. If the radii of the ends of a bucket, 45 cm high are 28 cm & 7 cm, determine the capacity & total surface area of bucket.
11. Water flows at the rate of 10 m per minute through a pipe having its diameter as 5 mm. How much time will it take to fill a conical vessel whose diameter of base is 40 cm & depth is 24 cm ?
12. Spherical marbles of diameter 1.4 cm each are dropped into a cylindrical beaker of radius 3.5 cm containing some water. Find the number of marbles that should be dropped into the beaker so that the water level rises by 5.6 cm.
13. A bucket is in the form of a frustum of a cone holds 28.49 litres of milk the radii of the top & bottom are 28 cm & 21 cm respectively. Find the height of the bucket.
14. From a solid cylinder whose height is 8 cm & radius 6 cm, a conical cavity of height 8 cm and of base radius 6 m is hollowed out. Find the volume of the remaining solid correct to two places of decimals. Also find the total surface area of the remaining solid. (take π = 3.1416)
15. A juice seller serves his customers using a glass. The inner diameter of the cylindrical glass is 5 cm, but the bottom of the glass has a hemispherical protion raised which reduces the capacity of the glass. If the height of the glass is 10 cm. Find the apparent capacity of the glass and is its actual capacity. (take π = 3.14)
16. An inverted cone of vertical height 12 cm & radius of base 9 cm contains water to a depth of 4 cm. Find the area of the interior surface of the cone not in contact with water. (use π = 22/7)
17. How many meters of cloth 1 m 10 cm wide, will be required to make a conical circus tent whose height is 12 m and radius of whose base is 10 m ? Also determine the cost of the cloth at Rs.7 per m.
18. The internal & external diameters of a hollow hemispherical vessel are 25 cm and 24 cm respectively. The cost of paint 1 cm2 of the surface is Rs.0.05. Find the total cost of painting the vessel.
19. The volumes of 2 spheres are in the ratio 64 : 27. Find their radii if sum of radii is 21 cm.
20. 3 cubes of metal whose edges are in the ratio 3 : 4 : 5 are melted down into a single cube whose diagonal is 312 cm. Find the edges of the three cubes.
Value Based Questions.
1. A manufacturer involved ten children in colouring playing top (lattu) which is shaped like a cone surmounted by a hemisphere. The entire top is 5 cm in height and the diameter of the top is 3.5 cm. Find the area they had to paint if 50 playing tops were given to them.
a) How is child labour an abuse for the society?
b) What steps can be taken to abolish child labour?
2 A teacher brings clay in the classroom to teach the topic “mensuration”. She forms a cylinder of radius 6 cm and height 8 cm with the clay. Then she moulds that cylinder into a sphere. Find the radius of the sphere formed.
a) Do teaching aids enhance teaching learning process? Justify your answer.
3. A night camp was organized for class X students for two days and their accommodation was planned in tents. Each tent is in the shape of a cylinder surmounted by a conical top. If the height and diameter of the cylindrical part are 2.1 m and 4 m respectively and the slant height of the top is 2.8 m., find the area of the canvas used for making the tent. Also, find the cost of the canvas of the tent at the rate of Rs. 500 per m2 (Note that the base of the tent will not be covered with canvas).
a) Is camping helpful to students in their development? Justify your answer.
4. A teacher brings clay in the classroom to teach the topic “mensuration”. She forms a cylinder of radius 6 cm and height 8 cm with the clay. Then she moulds that cylinder into a sphere. Find the radius of the sphere formed.
b) Do teaching aids enhance teaching learning process? Justify your answer.
5. A night camp was organized for class X students for two days and their accommodation was planned in tents. Each tent is in the shape of a cylinder surmounted by a conical top. If the height and diameter of the cylindrical part are 2.1 m and 4 m respectively and the slant height of the top is 2.8 m., find the area of the canvas used for making the tent. Also, find the cost of the canvas of the tent at the rate of Rs. 500 per m2 (Note that the base of the tent will not be covered with canvas).
b) Is camping helpful to students in their development? Justify your answer.
6. An ice cream seller gives ice cream in cylindrical cups of radius 8 cm and height 15 cm. He offers his customers the ice-cream in two conical cups of same radius and height instead of cylindrical cup for the same price. Is the ice cream seller giving the same quantity of ice cream in the same amount? Justify your answer.
Which human value is the ice- cream seller violating?
7. A milk container is made of a metal sheet in the form of a frustum of a cone of height 16 cm with radii of its lower and upper ends as 8 cm and 20 cm respectively. Find the cost of milk which the container can hold when fully filled at Rs. 20 per litre and the cost of the metal sheet used in making the container, at Rs. 8 per 100cm2 (Take π = 3.14)
If the milkman uses plastic sheet instead of metal sheet at the rate of Rs. 2 per 100cm2 to reduce his cost, find the cost of the plastic sheet used to make the container. Is his act justifying? Why should we reduce the use of plastics?
8. A teacher prepares a conical bucket as a teaching aid for her lesson. If the radii of the circular ends of the teaching aid which is 45 cm high are 28 cm and 7 cm, find the area of the sheet used in the teaching aid and it capacity.How does teaching aid contribute to the teaching – learning process? Give at least two ways
9. Harshit donates some part of his income to an orphanage every month. In a particular month, he wishes to donate toys for the children. Each toy is in the form of a cone mounted on a hemisphere of common base radius 7 cm. The total height of the toy is 31 cm. Find the total surface area of the toy. Also find the cost of 50 such toys if the cost of material used in the toy is Rs. 5 per 100cm2 and the cost of making is Rs. 10 per toy [Use π = 22/ 7 ]
What value of Harshit are reflected here? Justify your answer.
Q.- A bird bath for garden in the shape of a cylinder with a hemispherical depression at one end (see figure). The height of the cylinder is 1.45 m and its radius is 30 cm.Find the total surface area of the bird-bath.
More question-
1.The lateral surface area of right circular cylinder with base radius 7cm and height 10 cm is:
2.The lateral surface area of cylinder is 176cm2 & base area 38.5cm2. Then its volume is
(A) 803cm3
(B) 380cm3
(C) 308cm3
(D) 830cm3
3.Ratio of curved surface areas of two cylinders with equal radii is:
(A) H2 : h2
(B) 2H : h
(C) H : h
(D) None
4.Two cubes of 12cm edge are joined end to end. Find the surface area of the resulting cuboid.
5.Three cubes of sides 6 cm edge are joined end to end. Find the surface area of the resulting cuboid.
6.A solid sphere of radius 6cm is melted and recast into small spherical balls each of diameter 0.6cm. Find the number of balls thus obtained.
7.How many spherical bullets can be made out of a solid cube of lead whose edge measures 55cm, each bullet being 10 cm in diameter?
8.The area of the base of a cone is 616 sq. cm. If its height is 48 cm then its total surface area is:
(A) 2681cm2
(B) 2861cm2
(C) 2816cm2
(D) None
9.Ratio of lateral surface areas of two cylinders with equal heights is .
(A) R : r
(B) H : h
(C) R2 : r2
(D) None
10.The perimeter of ends of a frustum are 48 cm and 36 cm. If the height of the frustum be 11 cm, find its volume.
(A) 1400cm3
(B) 1500cm3
(C) 1554cm3
(D) 1600 cm
11.Find the maximum volume of a cone that can be curved out of a solid hemisphere of radius r.
(A) (4/3) πr2
(B) (1/3) πr3
(C) (1/3) πr2h
(D) None of these
12.A circus tent is in the form of a cone over a cylinder. The diameter of the base is 9 m, the height of cylindrical part is 4.8 m & the total height of the tent is 10.8 m. The canvass required for the tent is:
(A) 241.84 m2
(B) 24.184 m2
(C) 2418.4m2
(D) None
13.A fez, the cap used by the turks is shaped like the frustum of a cone. If its radius on the open side is 10cm, radius at the upper base is 4cm and its slant height is 15cm, find the area of material used for making it.
(A) 760cm2
(B) 710(2/7)cm2
(C) 731(2/7)cm2
(D) None of these
14.Determine the ratio of the volume of a cube to that of a sphere which will exactly fit inside the cube.
(A) 1:1
(B) 2: π
(C) π :5
(D) 6: π
15.If the radii of the circular ends of a conical bucket are 28 cm and 7 cm & height is 45 cm. The capacity of the bucket is:
(A) 48105cm2
(B) 48510cm2
(C) 48150cm2
(D) None
16.A cuboidal metal of dimensions 44cm × 30cm × 15cm was melted & cast into a cylinder of height 28 cm its radius is:
(A) 10 cm
(B) 20 cm
(C) 15 cm
(D) None
17.Find the volume of the largest right circular cone that can be cut out of a cube whose edge is 9 cm.
(A) 170 cm3
(B) 180.5 cm3
(C) 190.76 cm3
(D) 190.93 cm3
18.The area of the base of a cone is 616 sq. cm. If its height is 48 cm then its total surface area is:
(A) 2681cm2
(B) 2861cm2
(C) 2816cm2
(D) None
19.A top is of the shape of a cone over a hemisphere. The radius of the hemisphere is 3.5 cm. The total height of the top is 15.5 cm. The total area of top is:
(A) 215.4cm2
(B) 21.45cm2
(C) 214.5cm2
(D) None
20.A hollow sphere of internal and external diameters 4 cm & 8 cm respectively is melted into a cone of base diameter 8 cm. Find the height of the cone.
(A) 14 cm
(B) 12 cm
(C) 16 cm
(D) None
21.If the radii of the circular ends of a conical bucket is 45cm high, are 28cm and 7cm, find the capacity of the bucket.
(A) 25390 cm3
(B) 32670 cm3
(C) 43209 cm3
(D) 48510 cm3
22.Liquid is full in a hemisphere of inner diameter 9cm. This is to poured into cylindrical bottles of diameter 3 cm & height 4 cm . The number of bottles required are:
(A) 54
(B) 45
(C) 50
(D) None
23.A cylinder, whose height is two-third of its diameter, has the same volume as a sphere of radius 4cm. Calculate the radius of the base of the cylinder.
(A) 2 cm
(B) 4 cm
(C) 6 cm
(D) 8 cm
24.The diameter of a garden roller is 1.4 m and it is 2 m long. How much area will it cover in 5 revolutions?
(A) 50 sq m
(B) 44 sq m
(C) 40 sq m
(D) 35 sq m
25.Spherical ball of diameter 21 cm, is melted and recasted into cubes, each of side 1 cm. Find the number of cubes thus formed.
(A) 4045
(B) 4380
(C) 4851
(D) 4982
26.Two cubes each of 10 cm edge are joined end to end. Find the surface area of the resulting cuboid.
(A) 900 cm2
(B) 1000 cm2
(C) 1100 cm2
(D) None of these
27.Two cubes each of 10 cm edge are joined end to end. Find the surface area of the resulting cuboid.
(A) 900 cm2
(B) 1000 cm2
(C) 1100 cm2
(D) None of these
28.A spherical ball of diameter 21 cm is melted and recasted into cubes each of side 1cm. Find the number of cubes thus formed.
(A) 5021
(B) 4531
(C) 4851
(D) None of these
29.Metallic spheres of radii 6cm, 8cm and 10cm respectively, are melted to form a single solid sphere. Find the radius of the resulting sphere.
(A) 8 cm
(B) 10 cm
(C) 12 cm
(D) 14 cm
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30.A cylindrical vessel of diameter 9 cm has some water in it. A cylindrical iron piece of diameter 6 cm & height 4.5 cm is dropped in it. After it was completely immersed, the raise in the level of water is:
31.With a bucket of radius 14 cm & height 16 cm, 27 buckets of lime was poured to form a conical heap. If its area is 5544 cm2, the canvass required to cover it is:
32.A piece of metal pipe is 77 cm long with inside diameter of the cross section is 4 cm. If the outer diameter is 4.5 cm & the metal weighs 8 gm/cu cm, the weight of pipe is:
33.The diameter of a copper sphere is 6 cm. The sphere is melted and is drawn into a long wire of uniform circular cross-section. If the length of the wire is 36 cm, find its radius.
34.A right circular cone is of height 8.4 cm and radius of its base is 2.1 cm.It is melted and recast into a sphere. Find the radius of the sphere.
35.Three cubes whose edges measure 3 cm, 4 cm and 5 cm respectively to form a single cube . Find its edge. Also, find surface area of the new cube.
36.A glass cylinder with diameter 20 cm has water to a height of 9 cm. A metal cube of 8 cm edge is immersed in it completely. Calculate the height by which water will rise in the cylinder.
37.A piece of metal pipe is 66 cm long with inside diameter of the cross section is 4 cm. If the outer diameter is 5.5 cm & the metal weighs 7 gm/cu cm, the weight of pipe is ........
38.The length of a cold storage is double its breadth. Its height is 3 meters. The areas of its four walls (including door) is 108 m . Find its volume.
39.A circus tent is cylindrical to a height of 3 m and conical above it. If its base radius is 52.5 m and slant height of a conical portion is 53 , find the area of the canvas required to make the tent.
40.The ratio of base radius and height of a cone is 3:4 . If the cost of smoothening the curved surface area at 5 paise / sq.cm is Rs.11550. Then volume of liquid is:
41.A drinking glass is in the shape of a frustum of a cone of height 14 cm. The diameter of its two circular ends are 4 cm and 2 cm. Find the capacity of the glass.
42.A metallic right circular cone of height 9 cm & base radius 7 cm is melted into a cuboid whose two sides are 11 cm & 6 cm. What is the third side of the cuboid?
43.The radii of the circular ends of a frustum of height 6 cm are 14 cm and 6 cm respectively. Find the lateral surface area and total surface area of the frustum.
44.The radii of the circular ends of a frustum of height 6 cm are 14 cm and 6 cm respectively. Find the lateral surface area and total surface area of the frustum.
45.A circus tent is cylindrical upto a height of 3 m and conical above it. If the diameter of the base is 105 m and the slant height of the conical part is 53 m, find the total canvas used in making the tent.
46.A vessel is in conical shape. If its volume is 33.264 lt. and height is 72 cm, the cost of repairing its CSA at Rs.12/sq.m is:
47.The total surface area of a cylinder is 220 sq.cm with height 6.5 cm. Then its volume is:
48.The largest sphere is curved out of a cube of a side 7 cm. Find the volume of the sphere.
49.From a circle of radius 15 cm a sector with 216° angle is cut out and its bounding radii are bent so as to form a cone. Then its volume:
50.The cost of painting the curved surface area of cone at Rs 5 cm2 is Rs 3520. Which of the following volume of the cone, if its slant height is 25cm ?
51.A hemispherical bowl of internal diameter 40 cm contains a liquid. This liquid is to be filled in cylindrical bottles of radius 4 cm and height 8 cm. How many bottles are required to empty the bowl?
52.A conical vessel whose internal radius is 6cm and height is 25cm is full of water. The water is emptied into a cylindrical vessel with internal radius 10cm. Find the height to which the water rises.
53.Determine the ratio of the volume of cube to that of a sphere which will exactly fit inside the cube.
54.The radii of the circular ends of a conical bucket which is 49cm high, are 35cm and 14cm. Find the capacity of the bucket.
55.Find the volume of the largest right circular cone that can be cut out of a cube whose edge is 10cm.
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56.An iron pillar has some part in the form of a right circular cylinder and remaining in the form of a right circular cone. The radius of the base of each of cone and cylinder is 8 cm. The cylindrical part is 240cm high and the conical part is 36cm high. Find the weight of the pillar if one cubic cm of iron weights 7.8 grams.
57.The interior of a building is in the form of a right circular cylinder of diameter 4.2m and height 4m surmounted by a cone. The vertical height of cone is 2.1m. Find the outer surface and volume of the building.
58.A circus tent is cylindrical upto a height of 3m and conical above. If the diameter of the base is 105m and vertical height of the conical part is 7.26 m. Find the total canvas used in making the tent.
59.A toy is in the shape of a right circular cylinder with a hemisphere on one end and cone on the other.
The radius and height of the cylindrical part are 5cm and 13cm respectively. The radii of the hemispherical and conical parts are the same as that of the cylindrical part. Find the surface area of the toy if the total height of the cone is 30cm.
60.A hollow cone is cut by a plane parallel to the base and the upper portion is removed. If the curved surface of the remainder is 8/9 of the curved surface of the whole cone. Find the ratio of the linesegment in which the cone's altitude is divided by the plane.
61.A sphere of diameter 7 cm is dropped in a right circular cylinder vessel partly filled with water. The diameter of the cylindrical vessel is 14 cm. If the sphere is completely submerged in water, by how much will the level of water rise in the cylindrical vessel?
Section A (1 mark each)
Question. The radius of a sphere is r cm. It is divided into two equal parts. Find the whole surface of the two parts.
Answer : (6πr2 cm2)
Question. 12 solid spheres of the same size are made by melting a solid metallic cylinder of base radius 1cm and height 1/3 of 48cm. Find the radius of each sphere.
Answer : (1cm)
Question. If the radius of the base of a right circular cylinder is halved, keeping the height same, find the ratio of the volume of the reduced cylinder to that of original cylinder.
Answer : (1 : 4)
Question. Three cubes of iron whose edges are 3cm, 4cm and 5cm, respectively are melted and formed into a single cube. Find the edge of the new cube so formed.
Answer : (6cm)
Question. Volumes of two spheres are in the ratio 64 : 27. Find the ratio of their surface areas.
Answer : (16 : 9)
Section B (2 marks each)
Question. A hemispherical bowl of internal radius 9cm is full with a liquid. This liquid is to be filled into cylindrical shaped bottles of diameter 3cm and height 4cm. How many bottles are necessary to empty the bowl?
Answer : (54)
Question. A cylindrical tank has a capacity of 6160cm. Find its depth if its radius is 14m. Also calculate the cost of painting its curved surface (outer) at a rate of ₹ 3 per m2.
Answer : a(Depth=5m; Cost= ₹ 1320)
Question. A glass cylinder with diameter 20cm has water to a height of 9cm. A metal cube of 8cm edge is immersed in it completely. Calculate the height by which water will rise in the cylinder.
Answer : (1.62cm)
Question. If a wire is bent into the shape of a square, then the area enclosed by the square is 81cm2. When the same wire is bent into a semi-circular shape, find the area enclosed by the semi-circle.
Answer : (77cm2)
Question. Find the volume (in cm3) of the largest right circular cone that can be cut off from a cube of edge 4.2cm.
Answer : (19.4cm3)
Section C (3 marks each)
Question. The circumference of the base of a conical tent is 44m. If the height of tent is 24m, find the length of the canvas used in making the tent, if the width of the canvas is 2m. (use π = 22/7)
Answer : (275m)
Question. A spherical shell of lead whose external and internal diameters are 24cm and 18cm respectively is melted and recast into a right circular cylinder 37cm high. Find the radius of the base of the cylinder.
Answer : (6cm)
Question. A rectangular sheet of paper of dimensions 44cm X 18cm is rolled along its length and a cylinder is formed. Find the volume of the cylinder so formed. (use π = 22/7)
Answer : (2772cm3)
Question. Find the volume of the largest solid right circular cone that can be cut out of a solid cube of side 14cm.
Answer : (719cm3)
Question. A solid right circular cylinder has a total surface of 462 sq. cm. Its curved surface area is one-third of its total surface area. Find the volume of the cylinder.
Answer : (539 cm3)
Section D (4 marks each)
Question. Water is flowing through a cylindrical pipe, of internal diameter 2cm, into a cylindrical tank of base radius 40cm, at the rate of 0.4 m/s. Determine the rise in level of water in the tank in half an hour.
Answer : (4.5 cm)
Question. A bucket open at the top and made up of a metal sheet is in the form of a frustum of a cone. The depth of the bucket is 24cm and the diameters of its upper and lower circular ends are 30cm and 10 cm respectively. Find the cost of metal sheet used in it at the rate of ₹ 10 per 100cm2. (use π = 3.14)
Answer : (₹ 171.13)
Question. A bucket is in the form of a frustum of a cone whose radii of the bottom and the top are 7cm and 28cm respectively. If the capacity of the bucket is 21560 cm3, find the whole surface area of the bucket.
Answer : (3344cm2)
Question. Water is flowing at the rate of 15km/hr through a cylindrical pipe of diameter 14cm into a cuboidal pond which 50m long and 44m wide. In what time the level of water in pond rise by 21cm?
Answer : (2hrs.)
Question. A right angled triangle, whose sides are 3cm, 4cm, and 5cm, is revolved about the longest side. Find the surface area of the figure (double cone) obtained.
Answer : (52.8cm2)
Question. A hollow cone is cut by a plane parallel to the base and the upper portion is removed. If the curved surface of the remainder is 8/9 of the curved surface of the whole cone, find the ratio of the line segments in which the altitude of the cone is divided by the plane.
Answer : (1 : 2)
Question. The height of a cone is 30cm. A small cone is cut off at the top by a plane parallel to the base. If its volume be (1/27)th of the volume of the given cone, at what height above the base is the section made?
Answer : (20 cm)
Question. A cone is divided into two parts by drawing a plane through the midpoint of its axis, parallel to its base. Compare the volumes of the two parts.
Answer : (1/7)
| CBSE Class 10 Mathematics Surface Area And Volume Worksheet |
Worksheet for CBSE Mathematics Class 10 Chapter 13 Surface Area and Volume
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