EduSahara™ Worksheet

Question 1

1.

From a solid cylinder of height 18.00 cm and base radius 6.00 cm, a conical cavity of height 9.00 cm and base radius 6.00 cm is drilled out. Find the volume of the resulting solid

(i)

1957.14 cu.cm
(ii)

1697.14 cu.cm
(iii)

1847.14 cu.cm
(iv)

1567.14 cu.cm
(v)

1617.14 cu.cm

Question 2

2.

A conical vessel, whose internal radius is 10.50 cm and height 20.00 cm, is full of liquid . Its contents are emptied into a cylindrical vessel with internal radius 7.00 cm. Find the height to which the liquid rises in the cylindrical vessel.

(i)

20.00 cm
(ii)

15.00 cm
(iii)

18.00 cm
(iv)

10.00 cm
(v)

12.00 cm

Question 3

3.

From a circular cylinder of diameter 15.00 cm and height 12.00 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)

1174.29 cu.cm
(ii)

1544.29 cu.cm
(iii)

1414.29 cu.cm
(iv)

1254.29 cu.cm
(v)

1464.29 cu.cm

Question 4

4.

A cone of maximum volume is carved out of a cube of edge 24.00 cm. Find the volume of the remaining material after the cone is carved out

(i)

11403.43 cu.cm
(ii)

10203.43 cu.cm
(iii)

8903.43 cu.cm
(iv)

10703.43 cu.cm
(v)

9503.43 cu.cm

Question 5

5.

A cone of maximum volume is carved out of a cuboid of dimensions 23.00 cm✕23.00 cm✕27.00 cm. Find the volume of the cone

(i)

4010.79 cu.cm
(ii)

3920.79 cu.cm
(iii)

3580.79 cu.cm
(iv)

3690.79 cu.cm
(v)

3740.79 cu.cm

Question 6

6.

An open cylindrical vessel of internal diameter 10.00 cm and height 23.00 cm stands on a horizontal table. Inside this is placed a solid metallic right circular cone, the diameter of whose base is 5.00 cm and height 23.00 cm and filled with water. If the cone is replaced by another cone whose height is 9.20 cm and base radius is 1.50 cm, find the drop in the water level.

(i)

9.64 cm
(ii)

0.64 cm
(iii)

3.64 cm
(iv)

2.64 cm
(v)

1.64 cm

Question 7

7.

A cylindrical vessel of base radius 20.00 cm contains water . A solid sphere of radius 14.00 cm is immersed completely in the water. Find the rise in the water level in the vessel

(i)

7.15 cm
(ii)

8.15 cm
(iii)

9.15 cm
(iv)

11.15 cm
(v)

10.15 cm

Question 8

8.

Marbles of diameter 1.80 cm are dropped into a cylindrical beaker containing some water. When they are fully submerged, the water level rises by 18 cm. If the diameter of the beaker is 32.40 cm, find the number of marbles that are dropped in it

(i)

5120
(ii)

4810
(iii)

4860
(iv)

5040
(v)

4680

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 10.00 cm and height is 20.00 cm. The radius of the hemisphere is 5.00 cm and the height of the cone is 13.00 cm. Find the volume of water left in the cylinder.

(i)

5553.33 cu.cm
(ii)

5683.33 cu.cm
(iii)

5843.33 cu.cm
(iv)

5443.33 cu.cm
(v)

5863.33 cu.cm

Question 10

10.

A conical vessel of radius 10.00 cm and height 24.00 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)

40
83
(ii)

40
79
(iii)

14
27
(iv)

40
81
(v)

38
81

Question 11

11.

A well of diameter 14.00 m is dug to a depth of 19.00 m and the soil from digging is evenly spread out to form a platform of base dimensions 22.00 m✕26.00 m . Find the height of the platform

(i)

4.12 m
(ii)

7.12 m
(iii)

3.12 m
(iv)

5.12 m
(v)

6.12 m

Question 12

12.

A well of diameter 14.00 m is dug to a depth of 11.00 m . The soil taken out of it has been spread evenly all around it in the shape of a circular ring of width 11m to form an embankment. Find the height of the embankment.

(i)

0.96 m
(ii)

1.96 m
(iii)

2.96 m
(iv)

3.96 m
(v)

9.96 m

Question 13

13.

An ice cream container has the shape of a right circular cylinder having inner diameter 34.00 cm and height 38.00 cm . The ice cream is filled into cones of diameter 14.00 cm and height 18.00 cm , having a hemispherical shape on the top. Find the number of such complete cones which can be filled with ice cream

(i)

21
(ii)

26
(iii)

24
(iv)

18
(v)

16

Question 14

14.

Water in a canal, 11 m wide and 5 m deep is flowing with a speed of 5 kmph . How much area will it irrigate in 10 min, if 10 cm of standing water is needed ?

(i)

466333.33 sq.m
(ii)

458333.33 sq.m
(iii)

470333.33 sq.m
(iv)

435333.33 sq.m
(v)

442333.33 sq.m

Question 15

15.

A farmer connects a pipe of internal diameter
64 cm

from a canal into a cylindrical tank in his field,

which is
16 m
in diameter and
4 m
deep.

If water flows through the pipe at the rate of
25
7

kmph
,

in how much time will the tank be filled ?

(i)

47.00 min
(ii)

37.00 min
(iii)

39.00 min
(iv)

42.00 min
(v)

45.00 min

Assignment Key