CBSE Class 10 Mathematics Worksheet
UNIT VI: Mensuration - Surface Areas And Volumes
1.
A solid metallic sphere of diameter 16 cm is melted and recast into a number of smaller cones each of radius 4 cm and height 8 cm. Find the number of cones so formed.
2.
Its is a decorative block, made up of two solid - a cube and a hemisphere. The base of the block is a cube of side 6cm and the hemisphere fixed on the top has a diameter of 3.5 cm Find the total surface area of the block.
3.
Volume of two sphere are in the ration 64:27. Find the ratio of their surface area.
4.
If the total surface area of a solid hemisphere is 
, find its volume.
5.
A solid metallic cylinder of radius 3.5 cm and height 14 cm is melted and recasted into a number of small solid metallic balls , each of radius 7/12 cm. Find the number of balls so formed.
6.
A solid metallic cone of radius 2 cm and height 8 cm is melted into a sphere. find the radius of sphere.
7.
From a solid cylinder of height 15 cm and diameter 16 cm a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid to nearest cm2
8.
A cubical block of side 10 cm is surmounted by a hemisphere. What is the largest diameter that the hemisphere can have? Find the cost of painting the total surface area of the solid so formed, at the rate of Rs 5 per 100 sq.cm (use ยต=3.14)
9.
The radii of the circular ends of a frustum of cone of height 6 cm are 14 cm and 6 cm. Find the lateral surface area and total surface area of the frustum
10.
The slant height of a frustum of a cone is 4 cm and the perimeter of its circular ends are 18 cm and 6 cm . Find the curved surface area of the frustum.
11.
The surface area of a cube whose volume is 64 is
A)
96 sq. cm
B)
64 sq. cm
C)
108 sq. cm
D)
72 sq. cm
12.
A toy is in the form of a cone of base radius 3.5 cm mounted on a hemisphere of base diameter 7 cm. If the total height of toy is 15.5 cm, find the total surface area of the toy.
13.
The ratio of the volumes of two spheres is 8:27. If r and R are the radii of spheres. then find the (R-r):r.
14.
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 volume of the remaining solid to the nearest 
.
15.
Water in a canal 6 m wide and 1.5 m deep is flowing with a speed of 10 km/h. How much area in hectare will irrigate in 30 mins if 8 cm of standing water is needed.
16.
A Metallic bucket open at the top of height 24 cm is in the form of rustum of cone, radii of whose lower and upper ends are 7 cm and 14 cm. Find the volume of the water that can fill the bucket and area of the metal sheets.
17.
A cylinder and a cone have base radii 5 cm and 3 cm and their respective heights are 4 cm and 8 cm. Find the ratio of there volumes.
18.
A solid toy is in the form of a hemisphere surmounted by a right circular cone.The height of the cone is 2 cm and the diameter of the base is 4 cm. Determine the volume of the toy. Find the difference of the volume of the cylinder and toy.
19.
A farmer connects a pipe of internal diameter 20 cm from a canal into a cylindrical tank in his field, which is 10 m in diameter and 2 m deep. If the water flows through the pipe at the rate of 3 km/hr., in how much time will the take get field.
20.
A 21 m deep well with diameter 6 m is dug and the earth from digging is evenly spread to from a platform 27 m*11 m. Find the height of the platform.
CBSE Class 10 Mathematics Worksheet
UNIT VI: Mensuration - Surface Areas And Volumes
Answers
1.
16
2.
225.625 cm sq.
3.
0.67291666666666661
4.
5.
648
6.
2 cm
7.
1383 cm sq. (approx.)
8.
33.93
9.
1357.71 cm sq.
10.
48 cm sq.
11.
Option A
12.
214.5 cm sq.
13.
4.3055555555555562E-2
14.
15.
56.25 hectare
16.
8616.16 liter // 2263.94 cm sq.
17.
25:6
18.
19.
100 mins
20.
2 m
