CBSE Class 10 Mathematics Surface Areas And Volumes Worksheet Set A

 

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)

 

 

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)

 

 

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)

 

 

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)