CBSE Class 10 Mathematics Surface Areas And Volumes Worksheet Set A

Read and download free pdf of CBSE Class 10 Mathematics Surface Areas And Volumes Worksheet Set A. 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

SURFACE AREAS AND VOLUMES
 

Question. A solid is in the shape of a cone mounted on a hemisphere of same base radius. If the curved surface areas of the hemispherical part and the conical part are equal, then find the ratio of the radius and the height of the conical part.
Answer : 1:√𝟑

Question. The surface area of a sphere is 616cm2. Find its radius.
Answer : 
7cm

Question. A toy is in the form of a cone mounted on a hemisphere of same radius 7 cm. If the total height of the toy is 31 cm, find its total surface area.
Answer : 
858 cm2

Question. Two cones with same base radius 8 cm and height 15 cm are joined together along their bases. Find the surface area of the shape so formed.
Answer : 
854(𝟔/𝟕)cm2

Question. A circus tent is in the form of a right circular cylinder with right circular cone above it. The
i. diameter and the height of the cylindrical part of the tent are 126m and 12m respectively. The total
ii. height of the tent is 28m. Find the total cost of the tent if the canvas used costs Rs.30 per sq.m.
Answer : Rs.528660

Question. The largest possible cylinder is cut out from a wooden cube of edge 8 cm. Find the volume of wood remaining in the cube.
Answer : 109.8 cm3

Question. A semi-circular sheet of paper of diameter 28 cm is bent into an open conical cup. Find the depth and capacity of the cup.
Answer : 718(𝟐/𝟑)cm3

Question. A solid sphere of diameter 14 cm is cut into two halves by a plane passing through the centre. Find the combined surface area of the two hemispheres so formed.
Answer : 924 cm2

Question. A tent is in the shape of a right circular cylinder up to a height of 300 cm and conical above it. The total height of the tent is 1350 cm and radius of its base is 1400cm. Find the cost of cloth required to make the tent at the rate of Rs.80 per square metre. (Take π= 22/7)
Answer : Rs.82720

Question. If the total surface area of a solid hemisphere is 462 cm2, find its radius.
Answer : 
7cm

Question. A wallpaper, 312m long and 25cm wide is required to cover the walls of a room. Length of the room is 7m and its breadth is twice its height. Determine the height of the room.
Answer : 
3m

Question. Find the volume of the greatest sphere that can be cut from a cylindrical log of wood of base radius 1 cm and height 5 cm.
Answer : 
4/3 𝜋

Question. Find the curved surface area of a right circular cone of height 15 cm and base diameter 16 cm.
Answer : 
136π

 
Section A 
 
1. The radius of a sphere is r cm. It is divided into two equal parts. Find the whole surface area of the two parts.
 
• (6πr2 cm2 - Board 2012) (HOTS)
 
2. 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.
 
• (1cm– Board 2012)
 
3. 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.
 
• (1 : 4 - Board 2012) (HOTS)
 
4. 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.
 
• (6cm - Board 2013)
 
5. Volumes of two spheres are in the ratio 64 : 27. Find the ratio of their surface areas.
 
• (16 : 9 - Board 2013)
 
Section B 
 
6. 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?
 
• (54 - Board 2012)
 
7. 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.
 
• (Depth=5m; Cost= ₹ 1320 - Board 2012)
 
8. 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.
 
• (1.62cm – Board 2012)
 
9. 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.
 
• (77cm2 – Board 2014)
 
Section C 
 
10. 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) (275m - Board 2013)
 
11. 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.
 
• (6cm - Board 2013)
 
12. 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) (2772cm3 -Board 2012)
 
13. Find the volume of the largest solid right circular cone that can be cut out of a solid cube of side 14cm.
 
• (719cm3 - Board 2014)

 

14. 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.
 
• (539 cm3 - Board 2014)(HOTS)
 
Section D 
 
15. 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.
 
•(4.5 cm - Board 2013)
 
16. 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 ∏=3.14)
 
•(₹ 171.13 - Board 2013)
 
17. 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.
 
• (3344cm2 - Board 2014)
 
18. 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?
 
• (2hrs. - Board 2012)
 
19. 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.
 
• (52.8cm2 - Board 2012)(HOTS)
 
20. 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.
 
• (1 : 2 - Board 2004)(EXEMPLAR)
 
21. 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?
 
• (20 cm - Board 2005)(EXEMPLAR)
 
22. 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. 
 
• (1/7- Board 2003) )(EXEMPLAR)
 
 

Please click on below link to download CBSE Class 10 Mathematics Surface Areas And Volumes Worksheet Set A

Chapter 13 Surface Area and Volume CBSE Class 10 Mathematics Worksheet

The above practice worksheet for Chapter 13 Surface Area and Volume has been designed as per the current syllabus for Class 10 Mathematics released by CBSE. Students studying in Class 10 can easily download in Pdf format and practice the questions and answers given in the above practice worksheet for Class 10 Mathematics on a daily basis. All the latest practice worksheets with solutions have been developed for Mathematics by referring to the most important and regularly asked topics that the students should learn and practice to get better scores in their examinations. Studiestoday is the best portal for Printable Worksheets for Class 10 Mathematics students to get all the latest study material free of cost. Teachers of studiestoday have referred to the NCERT book for Class 10 Mathematics to develop the Mathematics Class 10 worksheet. After solving the questions given in the practice sheet which have been developed as per the latest course books also refer to the NCERT solutions for Class 10 Mathematics designed by our teachers. After solving these you should also refer to Class 10 Mathematics MCQ Test for the same chapter. We have also provided a lot of other Worksheets for Class 10 Mathematics which you can use to further make yourself better in Mathematics.

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