CBSE Class 10 Mathematics Surface Areas And Volumes Worksheet Set C

Read and download free pdf of CBSE Class 10 Mathematics Surface Areas And Volumes Worksheet Set C. Download printable Mathematics Class 10 Worksheets in pdf format, CBSE Class 10 Mathematics Chapter 13 Surface Area and Volume Worksheet has been prepared as per the latest syllabus and exam pattern issued by CBSE, NCERT and KVS. Also download free pdf Mathematics Class 10 Assignments and practice them daily to get better marks in tests and exams for Class 10. Free chapter wise worksheets with answers have been designed by Class 10 teachers as per latest examination pattern

Chapter 13 Surface Area and Volume Mathematics Worksheet for Class 10

Class 10 Mathematics students should refer to the following printable worksheet in Pdf in Class 10. This test paper with questions and solutions for Class 10 Mathematics will be very useful for tests and exams and help you to score better marks

Class 10 Mathematics Chapter 13 Surface Area and Volume Worksheet Pdf

Question. A cylindrical pencil sharpened at one edge is the combination of
(a) a cone and a cylinder
(b) cube and a cylinder
(c) a hemisphere and a cylinder
(d) two cylinders
Answer : A

Question. A solid ball is exactly fitted inside the cubical box of side a. The volume of the ball is
(a) (1/6)πa3
(b) (4/3)πa3
(c) (1/3)πa3
(d) None of these
Answer : A

Question. A cubical icecreambrick of edge 22 cmis to be distributed among some children by filling icecream cones of radius 2 cm and height 7 cm upto its brim. How many children will get icecream cones?
(a) 163
(b) 263
(c) 363
(d) 463
Answer : C

Question. The shape of a gilli, in the gilli-danda game (see figure) is a combination of

(a) two cylinders
(b) a cone and a cylinder
(c) two cones and a cylinder
(d) two cylinders and a cone
Answer : C

Question. If two solid hemispheres of same base radius r are joined together along their bases, then curved surface area of this new solid is
(a) 4πr2
(b) 6πr2
(c) 3πr2
(d) 8πr2
Answer : A

Question. A solid cylinder of radius r and height h is placed over other cylinder of same height and radius.
The total surface area of the shape so formed is

(a) 4πr(h2 + r2)
(b) 4πr[h + r]
(c) 4π(h2 + r2)
(d) None of the above
Answer : D

Question. The capacity of a cylindrical vessel with a hemispherical portion raised upward at the bottom as shown in the figure is πr2/2 [3h − 2r].

""CBSE-Class-10-Mathematics-Surface-Areas-And-Volumes-Worksheet-Set-C

Answer : C

Question. A surahi is the combination of
(a) a sphere and a cylinder
(b) a hemisphere and a cylinder
(c) two hemispheres
(d) a cylinder and a cone
Answer : A

 

Question. Three cubes each of side 5 cm are joined end to end, then the surface area of the resulting solid is
(a) 250 cm2
(b) 180 cm2
(c) 350 cm2
(d) None of these
Answer : C

Question. A right circular cylinder of radius r cm and height h cm(where, h > 2r) just encloses a sphere of diameter
(a) r cm
(b) 2r cm
(c) h cm
(d) 2h cm
Answer : B

Question. Two cones have their heights in the ratio 1 : 3 and radii in the ratio 3: 1, then the ratio of their volumes is
(a) 1 : 3
(b) 3 : 1
(c) 2 : 3
(d) 3 : 2
Answer : B

Question. From a solid circular cylinder with height 10 cm and radius of the base 6 cm, a right circular cone of the same height and same base is removed, then the volume of remaining solid is
(a) 280 π cm3
(b) 330 π cm3
(c) 240 π cm3
(d) 440 π cm3
Answer : C

Question. A plumbline (sahul) is the combination of (see figure)

""CBSE-Class-10-Mathematics-Surface-Areas-And-Volumes-Worksheet-Set-C-1

(a) a cone and a cylinder
(b) a hemisphere and a cone
(c) cube and a cylinder
(d) sphere and cylinder
Answer : B

Question. A solid cone of radius r and height h is placed over a solid cylinder having same base radius and height as that of a cone. The total surface area of the combined solid is
(a) πrl + 2πrh
(b) πr2 (1 + 2h)
(c) πr[√r2 + h2 + 2h + r]
(d) None of these
Answer : C

Question. Marbles of diameter 1.4 cm are dropped into a cylindrical beaker of diameter 7 cm containing some water. The water level rises by 5.6 cm. When marble dropped into the beaker, then the number of marble is
(a) 150
(b) 160
(c) 175
(d) 235
Answer : A

Question. The diameter of a sphere is 6 cm. It is melted and drawn into a wire of diameter 2 mm.
The length of the wire is

(a) 12 m
(b) 18 m
(c) 36 m
(d) 66 m
Answer : C

Question. During conversion of a solid from one shape to another, the volume of the new shape will
(a) increase
(b) decrease
(c) remain unaltered
(d) be doubled
Answer : C

Question. A heap of rice is in the formof a cone of base diameter 24 m and height 3.5 m. Find the volume of the rice. How much canvas as cloth is required to just cover the heap? 
(a) 105.5 m2
(b) 471.42 m2
(c) 173.5 m2
(d) None of these
Answer : B

Question. A 20 m deep well, with diameter 7 m is dug and the earth from digging is evently spread out to form a platform 22 m by 14 m. The height of the platform is 
(a) 2.5 m
(b) 3.5 m
(c) 3 m
(d) 2 m
Answer : A

Question. If the radius of the base of a right circular cylinder is halved, keeping the height same, then find the ratio of the volume of the cylinder thus obtained to the volume of original cylinder. 
(a) 1/3
(b) 1/4
(c) 1/2
(d) 1/5
Answer : B

Question. A mason constructs a wall of dimensions 270 cm× 300 cm× 350 cmwith the bricks each of size 22.5 cm × 11.25 cm× 8.75 cmand 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
Answer : B

Question. A wooden article was made by scooping out a hemisphere from each end of a solid cylinder, as shown in figure. If the height of the cylinder is 10 cm and its base is of radius 3.5 cm. Find the total surface area of the article.

(a) 374 cm2
(b) 370 cm2
(c) 475 cm2
(d) None of these
Answer : A

Case Based MCQs

A. To make the learning process more interesting creative and innovative Shavya’s class teacher brings clay in the classroom, to teach the topic. Surface Areas and Volumes. With clay, she forms a cylinder of radius 4 cm and height 18 cm. Then, she moulds the cylinder into a sphere and ask some question to students.

Question. The radius of the sphere so formed is
(a) 4 cm
(b) 6 cm
(c) 7 cm
(d) 8 cm
Answer : B

Question. The volume of the sphere so formed is
(a) 905.14 cm3
(b) 903.27 cm3
(c) 1296.5 cm3
(d) 1156.63 cm3
Answer : A

Question. Find the ratio of the volume of sphere to the volume of cylinder.
(a) 2 : 1
(b) 1 : 2
(c) 1 : 1
(d) 3 : 1
Answer : C

Question. Total surface area of the cylinder is
(a) 553.14 cm2
(b) 751.52 cm2
(c) 625 cm2
(d) 785.38 cm2
Answer : A

Question. During the conversion of a solid from one shape to another the volume of new shape will
(a) be increase
(b) be decrease
(c) remain unaltered
(d) be double
Answer : C

B. Geeta and Meena have 10 and 6 CD respectively, each of radius 4 cm and thickness 1 cm. They place their CD one above the other to form solid cylinders.

""CBSE-Class-10-Mathematics-Surface-Areas-And-Volumes-Worksheet-Set-C-5

Based on the above information, answer the following questions.

Question. Curved surface area of the cylinder made by Geeta is
(a) 308.17 cm2
(b) 132 cm2
(c) 154 cm2
(d) 251.42 cm2
Answer : D

Question. The ratio of curved surface area of the cylinder made by Geeta and Meena is
(a) 3 : 5
(b) 3 : 2
(c) 5 : 3
(d) 5 : 7
Answer : C

Question. The volume of the cylinder made by Meena is
(a) 301.44 cm3
(b) 144 cm3
(c) 132 cm3
(d) 208.42 cm3
Answer : A

Question. The ratio of the volume of the cylinders made by Geeta and Meena is
(a) 1 : 2
(b) 2 : 5
(c) 3 : 5
(d) 5 : 3
Answer : D

Question. When two CD Cassette are shifted from Geeta cylinder to Meena’s cylinder, then
(a) Volume of two cylinder become equal
(b) Volume of Geeta’s cylinder > Volume of Meena’s cylinder
(c) Volume of Meena’s cylinder > Volume of Geeta’s cylinder
(d) None of the above
Answer : A

C. The Great Stupa at Sanchi is one of the oldest stone structures in India, and an important monument of
Indian Architecture. It was originally commissioned by the emperor Ashoka in the 3rd century BCE. Its nucleus was a simple hemispherical brick structure built over the relics of the Buddha. It is a perfect example of combination of solid figures. A big hemispherical dome with a cuboidal structure mounted on it.
(take π = 22/7)

""CBSE-Class-10-Mathematics-Surface-Areas-And-Volumes-Worksheet-Set-C-6

Question. The cloth require to cover the hemispherical dome if the radius of its base is 14m is
(a) 1222 sq m
(b) 1232 sq m
(c) 1200 sq m
(d) 1400 sq m
Answer : B

Question. The total surface area of the combined figure i.e. hemispherical dome with radius 14 m and cuboidal shaped top with dimensions 8 m × 6 m × 4 m is
(a)1200 sq m
(b) 1232 sq m
(c) 1392 sq m
(d) 1932 sq m
Answer : C

Question. Calculate the volume of the hemispherical dome if the height of the dome is 21 m.
(a) 19404 cu m
(b) 2000 cu m
(c) 15000 cu m
(d) 19000 cu m
Answer : A

Question. The formula to find the volume of sphere is
(a) (2/3)πr3
(b) (4/3)πr3
(c) 4πr2
(d) 2πr2
Answer : B

Question. The volume of the cuboidal shaped top is with dimensions mentioned in question (iv).
(a) 182.45 m3
(b) 282.45 m3
(c) 292 m3
(d) 192
Answer : D

 

 

 

 

 

 

SURFACE AREAS AND VOLUMES
 
SECTION A: 
 
1. A cone and a cylinder are of same height. If the radii of their bases are in the ratio 3 : 5, then find the ratio of their volumes .
 
2. Find the base area of the cylinder of radius 7 cm.
 
3. If the radius of a sphere is 2 cm, then find the curved surface area of the sphere.
 
4. The surface area of the sphere is 2464 sq.cm. Find its radius.
 
5. How many litres of water will a hemispherical tank hold whose diameter is 4.2 m?
 
6. Radius and slant height of a cone are 20 cm and 29 cm respectively. Find its volume.
 
7. The surface area of the sphere is 2464 sq.cm. Find its radius.
 
8. The diameter of the base of a right circular cylinder is r and its height is equal to the radius of its base. Find the volume of the cylinder.
 
9. If the circumference of the base of a solid right circular cone is 236 cm and its slant height is 12ncm, find its curved surface area.
 
10. A sphere and a cube are of same height, find the ratio of their volumes if π = 22/7
 
SECTION B: 
 
11. A hemispherical bowl of radius 7 cm is full with water. The water from the bowl is to be emptied into a cylindrical vessel of radius 3.5 cm. Calculate the height of cylindrical vessel.
 
12. A solid metallic sphere of radius 21 cm is melted and recasted to a no. of cones with radius 7 cm and height 28 cm. Find the no. of cones so formed.
 
13. A hemispherical iron of radius 14 cm is cast into a right circular cone of radius 98 cm. Find the height of cone.
 
14. The C.S.A of hemisphere is 154 cm2. Find its volume.
 
15. The volume of the sphere is numerically equal to its surface area. Find its diameter.
 
16. The radius and the height of the cylinder are in the ratio 2:7. If the curved surface area of the cylinder is 352 sq.cm, find it radius.
 
17. The radius of a wooden hemisphere is 10 cm. What is the its volume?
 
18. The perimeters of the ends of a frustum of a cone are 88 cm and 8.4 π cm. If the depth is 14 cm, then find its volume.
 
19. A solid cuboid of iron with dimensions 45 cm × 11 cm is melted and recast into a cylinder pipe. The outer & inner diameters are 10 cm and 8 cm respectively. Find the length of pipe.
 
20. 120 spherical marbles each of diameter 2.1 cm are dropped into a cylindrical vessel of diameter 7 cm containing some water which are completes immersed in water. What is the rise in level of water in vessel?
 
SECTION C: 
 
21. A tent is in the form of a cylinder surmounted by a conical top. If the height and radius of cylindrical part are 2.8 m and 2 m and slant height of the top is 3.2 m, find the area of canvas used for the tent.
 
22. A sphere of radius 5 cm is dropped into a cylindrical vessel partly filled with water. The diameter of the base of vessel is 20 cm. If the sphere is completely submerged, find the rise of level of water.
 
23. 168 cones each of diameter 7 cm and height 6 cm are melted to form a metallic hemisphere. Find the radius of hemisphere and the total surface area.
 
24. A well of diameter 10 m is 21 m deep is dug out and the earth from it is evenly spreaded to form a platform 20 m by 16 m. Find the height of plat form.
 
25. A bucket is in the shape of a frustum of a cone & holds 18.304 litres of water. The radii of top & bottom are 24 cm and 20 cm respectively, find the height of the bucket.
 
26. Water flows through a cylindrical pipe, of internal diameter 4 cm into a cylindrical tank of base radius 30 cm at the rise of 0.5 m/s. Find the rise in level of water in the tank in 2 hours.
 
27. From a solid cylinder of height 8 cm and base diameter 10 cm, a conical cavity of same height and same base diameter is hollowed out. What is the total surface area of the remaining solid.
 
28. A spherical tank with diameter 4 m full of water is to be emptied by a pipe at the rate of 5 2/7 litre per second. How much time will it take to make the tank one third empty.
 
29. Volume of cylinder is 896 π with height 14 cm. Find the total surface area of cylinder.
 
30. A cylindrical container has diameter 12 cm and height 15 cm is full with ice cream. The ice cream is to be filled into cones of height 12 cm & diameter 6 cm with hemispherical top. Find the no. of cones which can be filled with ice cream.
 
SECTION D: 
 
31. The radii of the circular ends of a bucket of height 15 cm are 7 cm and R. If the volume of bucket is 5390 cm3 find R.
 
32. A copper rod of diameter 4 cm and length 8 cm is drawn into a wire of length 40 m of uniform thickness. Find the thickness of the wire.
 
33. A sector of circle of radius 15 cm has the angle 120°. It is rolled up so that two boundary radii are joined together to form a cone. Find the volume of cone.
 
34. Using clay, a student made a right circular cone of height 48 cm and base radius 12 cm. Another student reshapes it in the form of a sphere. Find the radius of the sphere.
 
35. The radii of the internal and external surfaces of a metallic spherical shell are 7 cm and 5 cm. It is melted & recast into a right circular cylinder of height 8 2/3 cm. Find the diameter of the base of the cylinder.
 
36. A conical vessel of ratio 12 cm and height 16 cm completely filled with water. A sphere is lowered into the water & its size is such that it touches the sides, as shown in figure1. Find the fraction of water that overflows.
CBSE Class 10 Mathematics Surface Areas And Volumes Worksheet Set C
 
37. A 10 m wide cloth is used to make a conical tent of base diameter 21 m & height 30 m. Find the cost of cloth used at the rate of Rs. 30 perimeter.
 
38. The circumference of the base and height of a right circular cylinder are 44 cm and 10 cm respectively. Find its volume, curved surface area and total surface area.
 
39. The height of circular cone is trisected by two planes running parallel to the base. Find the ratio of the volumes of the three cones thus formed.
 
40. Water flows through a cylindrical pipe of internal radius 3.5 cm at 5 m per sec. calculate the volume of water in litres discharged by the pipe in one minute.

 

 

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