EduSahara™ Worksheet

Question 1

1.

From a solid cylinder of height 12.00 cm and base radius 6.00 cm, a conical cavity of height 7.00 cm and base radius 6.00 cm is drilled out. Find the volume of the resulting solid

(i)

1023.71 cu.cm
(ii)

1233.71 cu.cm
(iii)

1213.71 cu.cm
(iv)

833.71 cu.cm
(v)

1093.71 cu.cm

Question 2

2.

A conical vessel, whose internal radius is 5.00 cm and height 16.00 cm, is full of liquid . Its contents are emptied into a cylindrical vessel with internal radius 2.00 cm. Find the height to which the liquid rises in the cylindrical vessel.

(i)

33.33 cm
(ii)

36.33 cm
(iii)

30.33 cm
(iv)

38.33 cm
(v)

28.33 cm

Question 3

3.

From a circular cylinder of diameter 14.00 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)

1540.00 cu.cm
(ii)

1780.00 cu.cm
(iii)

1380.00 cu.cm
(iv)

1570.00 cu.cm
(v)

1420.00 cu.cm

Question 4

4.

A cone of maximum volume is carved out of a cube of edge 20.00 cm. Find the volume of the remaining material after the cone is carved out

(i)

6054.76 cu.cm
(ii)

5884.76 cu.cm
(iii)

5724.76 cu.cm
(iv)

5904.76 cu.cm
(v)

6034.76 cu.cm

Question 5

5.

A cone of maximum volume is carved out of a cuboid of dimensions 9.00 cm✕9.00 cm✕27.00 cm. Find the volume of the remaining material after the cone is carved out

(i)

1754.21 cu.cm
(ii)

1484.21 cu.cm
(iii)

1694.21 cu.cm
(iv)

1494.21 cu.cm
(v)

1614.21 cu.cm

Question 6

6.

An open cylindrical vessel of internal diameter 27.00 cm and height 27.00 cm stands on a horizontal table. Inside this is placed a solid metallic right circular cone, the diameter of whose base is 13.50 cm and height 27.00 cm and filled with water. If the cone is replaced by another cone whose height is 18.90 cm and base radius is 3.38 cm, find the drop in the water level.

(i)

3.86 cm
(ii)

9.86 cm
(iii)

1.86 cm
(iv)

0.86 cm
(v)

2.86 cm

Question 7

7.

A cylindrical vessel of base radius 26.00 cm contains water . A solid sphere of radius 19.00 cm is immersed completely in the water. Find the rise in the water level in the vessel

(i)

10.53 cm
(ii)

18.53 cm
(iii)

13.53 cm
(iv)

16.53 cm
(v)

8.53 cm

Question 8

8.

Marbles of diameter 1.00 cm are dropped into a cylindrical beaker containing some water. When they are fully submerged, the water level rises by 10 cm. If the diameter of the beaker is 20.00 cm, find the number of marbles that are dropped in it

(i)

5840
(ii)

6000
(iii)

6140
(iv)

5870
(v)

6150

Question 9

9.

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 27.50 cm. The radius of the hemisphere is 7.50 cm and the height of the cone is 20.00 cm. Find the volume of water left in the cylinder.

(i)

13241.96 cu.cm
(ii)

9741.96 cu.cm
(iii)

11441.96 cu.cm
(iv)

9141.96 cu.cm
(v)

11841.96 cu.cm

Question 10

10.

A conical vessel of radius 3.00 cm and height 4.00 cm is completely filled with water. A sphere is lowered into the water and its size is such that when it touches the sides, it is just immersed. Find the fraction of the water that overflows

(i)

3
10
(ii)

3
8
(iii)

1
2
(iv)

1
8
(v)

5
8

Question 11

11.

A well of diameter 10.00 m is dug to a depth of 14.00 m and the soil from digging is evenly spread out to form a platform of base dimensions 24.00 m✕18.00 m . Find the height of the platform

(i)

3.55 m
(ii)

1.55 m
(iii)

4.55 m
(iv)

0.55 m
(v)

2.55 m

Question 12

12.

A well of diameter 16.00 m is dug to a depth of 19.00 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)

0.62 m
(ii)

1.62 m
(iii)

2.62 m
(iv)

4.62 m
(v)

3.62 m

Question 13

13.

An ice cream container has the shape of a right circular cylinder having inner diameter 40.00 cm and height 50.00 cm . The ice cream is filled into cones of diameter 12.00 cm and height 15.00 cm , having a hemispherical shape on the top. Find the number of such complete cones which can be filled with ice cream

(i)

58
(ii)

61
(iii)

56
(iv)

66
(v)

64

Question 14

14.

Water in a canal, 11 m wide and 2 m deep is flowing with a speed of 16 kmph . How much area will it irrigate in 45 min, if 4 cm of standing water is needed ?

(i)

6570000.00 sq.m
(ii)

6600000.00 sq.m
(iii)

6420000.00 sq.m
(iv)

6720000.00 sq.m
(v)

6660000.00 sq.m

Question 15

15.

A farmer connects a pipe of internal diameter
20 cm

from a canal into a cylindrical tank in his field,

which is
4 m
in diameter and
5 m
deep.

If water flows through the pipe at the rate of
5
3

kmph
,

in how much time will the tank be filled ?

(i)

75.00 min
(ii)

69.00 min
(iii)

67.00 min
(iv)

77.00 min
(v)

72.00 min

Assignment Key