EduSahara™ Worksheet

Question 1

1.

A solid consisting of a right circular cone, standing on a hemisphere is placed upright, in a right circular cylinder full of water and touches the bottom. The radius of the cylinder is 12.50 cm and height is 23.50 cm. The radius of the hemisphere is 8.50 cm and the height of the cone is 10.00 cm. Find the volume of water left in the cylinder.

(i)

9646.54 cu.cm
(ii)

9496.54 cu.cm
(iii)

9366.54 cu.cm
(iv)

9316.54 cu.cm
(v)

9636.54 cu.cm

Question 2

2.

A well of diameter 19.00 m is dug to a depth of 17.00 m . The soil taken out of it has been spread evenly all around it in the shape of a circular ring of width 15m to form an embankment. Find the height of the embankment.

(i)

5.01 m
(ii)

2.01 m
(iii)

4.01 m
(iv)

3.01 m
(v)

1.01 m

Question 3

3.

If the vertical height of a cone is 9.00 cm and volume is 603.43 cu.cm, its T.S.A is

(i)

517.86 sq.cm
(ii)

521.86 sq.cm
(iii)

488.86 sq.cm
(iv)

496.86 sq.cm
(v)

503.86 sq.cm

Question 4

4.

If the slant height of a cone is 11.18 cm and vertical height is 5.00 cm, its volume is

(i)

511.81 cu.cm
(ii)

536.81 cu.cm
(iii)

523.81 cu.cm

Question 5

5.

The height of a right circular cone is 27.00 cm and the radius of its base is 7.50 cm. It is melted and recast into a right circular cone with base radius 5.25 cm. Find the new height

(i)

52.10 cm
(ii)

58.10 cm
(iii)

55.10 cm
(iv)

50.10 cm
(v)

60.10 cm

Question 6

6.

From a circular cylinder of diameter 11.00 cm and height 15.00 cm, a conical cavity of the same base radius and of the same height is hollowed out. Find the volume of the remaining solid.

(i)

950.71 cu.cm
(ii)

925.71 cu.cm
(iii)

972.71 cu.cm
(iv)

968.71 cu.cm
(v)

933.71 cu.cm

Question 7

7.

Water in a canal, 19 m wide and 4 m deep is flowing with a speed of 18 kmph . How much area will it irrigate in 50 min, if 5 cm of standing water is needed ?

(i)

24100000.00 sq.m
(ii)

22800000.00 sq.m
(iii)

25400000.00 sq.m
(iv)

21500000.00 sq.m
(v)

21300000.00 sq.m

Question 8

8.

If the slant height of a cone is 10.63 cm and vertical height is 7.00 cm, its base radius is

(i)

7.00 cm
(ii)

9.00 cm
(iii)

10.00 cm
(iv)

6.00 cm
(v)

8.00 cm

Question 9

9.

If the base radius of a cone is 7.00 cm and vertical height is 9.00 cm, its base area is

(i)

127.00 sq.cm
(ii)

138.00 sq.cm
(iii)

156.00 sq.cm
(iv)

154.00 sq.cm
(v)

179.00 sq.cm

Question 10

10.

If the base radius of a cone is 10.00 cm and T.S.A is 665.66 sq.cm, its base area is

(i)

342.29 sq.cm
(ii)

329.29 sq.cm
(iii)

302.29 sq.cm
(iv)

314.29 sq.cm
(v)

288.29 sq.cm

Question 11

11.

If the radius of a sphere is 10.00 cm, its T.S.A is

(i)

1217.14 sq.cm
(ii)

977.14 sq.cm
(iii)

1527.14 sq.cm
(iv)

1257.14 sq.cm
(v)

1377.14 sq.cm

Question 12

12.

If the vertical height of a cone is 5.00 cm and volume is 523.81 cu.cm, its base area is

(i)

289.29 sq.cm
(ii)

342.29 sq.cm
(iii)

314.29 sq.cm
(iv)

317.29 sq.cm
(v)

310.29 sq.cm

Question 13

13.

From a solid cylinder of height 16.00 cm and base radius 6.00 cm, a conical cavity of height 5.00 cm and base radius 6.00 cm is drilled out. Find the volume of the resulting solid

(i)

1621.71 cu.cm
(ii)

1381.71 cu.cm
(iii)

1661.71 cu.cm
(iv)

1441.71 cu.cm
(v)

1891.71 cu.cm

Question 14

14.

A conical vessel, whose internal radius is 9.50 cm and height 14.00 cm, is full of liquid . Its contents are emptied into a cylindrical vessel with internal radius 5.00 cm. Find the height to which the liquid rises in the cylindrical vessel.

(i)

11.85 cm
(ii)

13.85 cm
(iii)

19.85 cm
(iv)

21.85 cm
(v)

16.85 cm

Question 15

15.

A cylindrical vessel of base radius 15.00 cm contains water . A solid sphere of radius 9.00 cm is immersed completely in the water. Find the rise in the water level in the vessel

(i)

6.32 cm
(ii)

3.32 cm
(iii)

5.32 cm
(iv)

2.32 cm
(v)

4.32 cm

Question 16

16.

A farmer connects a pipe of internal diameter
54 cm

from a canal into a cylindrical tank in his field,

which is
18 m
in diameter and
3 m
deep.

If water flows through the pipe at the rate of
100
21

kmph
,

in how much time will the tank be filled ?

(i)

47.00 min
(ii)

45.00 min
(iii)

42.00 min
(iv)

39.00 min
(v)

37.00 min

Question 17

17.

A hemispherical depression is cut out from both ends of a cylinder. The height of the cylinder is 30.00 cm and its radius is 7.00 cm. Find the total surface area of the solid

(i)

2096.00 sq.cm
(ii)

1816.00 sq.cm
(iii)

1936.00 sq.cm
(iv)

1856.00 sq.cm
(v)

1966.00 sq.cm

Question 18

18.

If the base radius of a cone is 10.00 cm and volume is 733.33 cu.cm, its vertical height is

(i)

5.00 cm
(ii)

7.00 cm
(iii)

6.00 cm
(iv)

9.00 cm
(v)

8.00 cm

Question 19

19.

Metallic spheres of radii 14.00 cm, 6.00 cm are melted to form a single solid sphere. Find the radius of the resulting sphere.

(i)

3
√

2958

cm
(ii)

5
√

2960

cm
(iii)

2960

cm
(iv)

3
√

2960

cm
(v)

3
√

2963

cm

Question 20

20.

The radii of the ends of a frustum of a right circular cone 7.00 cm high are 12.00 cm and 7.00 cm. Its slant height is

(i)

7.60 cm
(ii)

8.60 cm
(iii)

9.60 cm
(iv)

10.60 cm
(v)

6.60 cm

Question 21

21.

If the base radius of a cone is 7.00 cm and slant height is 9.22 cm, its vertical height is

(i)

5.00 cm
(ii)

8.00 cm
(iii)

4.00 cm
(iv)

7.00 cm
(v)

6.00 cm

Question 22

22.

If the base radius of a cone is 6.00 cm and vertical height is 10.00 cm, its L.S.A. is

(i)

243.87 sq.cm
(ii)

204.87 sq.cm
(iii)

222.87 sq.cm
(iv)

201.87 sq.cm
(v)

219.87 sq.cm

Question 23

23.

If the T.S.A of a sphere is 1018.29 sq.cm, its volume is

(i)

3284.86 cu.cm
(ii)

2904.86 cu.cm
(iii)

3094.86 cu.cm
(iv)

2834.86 cu.cm
(v)

3054.86 cu.cm

Question 24

24.

If the slant height of a cone is 13.45 cm and T.S.A is 737.00 sq.cm, its vertical height is

(i)

7.00 cm
(ii)

10.00 cm
(iii)

8.00 cm
(iv)

9.00 cm
(v)

11.00 cm

Question 25

25.

If the base radius of a cone is 8.00 cm and T.S.A is 452.57 sq.cm, its L.S.A. is

(i)

226.43 sq.cm
(ii)

251.43 sq.cm
(iii)

269.43 sq.cm
(iv)

239.43 sq.cm
(v)

268.43 sq.cm

Assignment Key