Practice Questions: Surface Areas and Volumes | Mathematics (Maths) Class 10 PDF Download

Questions

1. If the ratio of volume of two spheres is 1:8, then find the ratio of their surface area.

2. Two cubes each of volume 64 cm³ are joined end to end. Find the surface area of the resulting cuboid.

3. Find the length of the longest rod that can be kept in a room of dimensions 12 cm × 9 cm × 8 cm. Hint: [Diagonal of Cuboid]

4. The decorative block shown in fig. is made of two solids-a cube and a hemisphere. The base of the block is a cube with edge 5 cm and the hemisphere fixed on the-top has a diameter of 4.2 cm. Find the total surface area of the block. [take π = 22/7] 

5. The radii of the circular ends of a bucket of height 15 cm are 14 cm and r cm (r < 14 cm). If the volume of bucket is 5390 cm³. Find the value of r. [Use π = 22/7]

6. From a solid cylinder whose height is 2.4 cm and diameter 1.4 cm, a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid. 

7. If the surface area of a sphere is 144 p cm², then what is its radius?

8. The radii of bases of cylinder and a cone are in the ratio 3 : 4 and their heights are in the ratio 2:3 then ratio between the volume of cylinder to volume of cone is?

9. If two identical cubes of side ‘a’ are joined end to end. Then the total surface area of resulting cuboid is ______.

10. A well of diameter 4 m is dug 21 m deep. The earth taken out of it has been spread evenly all around it in the shape of a circular ring of width 3 m to form an embankment. Find the height of the embankment.

11. The sum of the radius of base and height of a solid right circular cylinder is 37 cm. If the total surface area of the solid cylinder is 1628 sq. cm, find the volume of the cylinder, (use π=22/7)

12. A right circular cone of radius 3 cm, has a curved surface area of 47.1 cm². Find the volume of the cone, (use π = 3.14)

13. If the total surface area of a solid hemisphere is 462 cm², find its volume.

14. A 5 m wide cloth is used to make a conical tent of base diameter 14 m and height 24 m. Find the cost of cloth used at the rate 25 rupees/ meter.

15. 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. 

Answers

1. Ratio = 1:4

2. 640 cm²

3. 17cm

4. Surface Area of Block = 163.86 cm²   

5. ∴ r =7 cm

6. Total surface area of remaining solid = 17.6 cm²    

7. Radius = 6 cm

8.  9:8

9. 10a² sq.units

10. 4m

11. 4620 cm³    

12. 37.68 cm³     

13. Volume of hemisphere = 718.67 cm³

14. Cost of cloth = 2750 rupees

15. Total surface area = 858 cm²

Answers