EduSahara™ Worksheet

Question 1

1.

From a solid cylinder of height 14.00 cm and base radius 5.50 cm, a conical cavity of height 4.00 cm and base radius 5.50 cm is drilled out. Find the volume of the resulting solid

(i)

1344.24 cu.cm
(ii)

1054.24 cu.cm
(iii)

1074.24 cu.cm
(iv)

1204.24 cu.cm
(v)

1324.24 cu.cm

Question 2

2.

A conical vessel, whose internal radius is 15.00 cm and height 19.00 cm, is full of liquid . Its contents are emptied into a cylindrical vessel with internal radius 9.00 cm. Find the height to which the liquid rises in the cylindrical vessel.

(i)

20.59 cm
(ii)

22.59 cm
(iii)

12.59 cm
(iv)

17.59 cm
(v)

14.59 cm

Question 3

3.

From a circular cylinder of diameter 12.00 cm and height 17.00 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)

1402.29 cu.cm
(ii)

1122.29 cu.cm
(iii)

1282.29 cu.cm
(iv)

1062.29 cu.cm
(v)

1352.29 cu.cm

Question 4

4.

A cone of maximum volume is carved out of a cube of edge 25.00 cm. Find the volume of the remaining material after the cone is carved out

(i)

11532.74 cu.cm
(ii)

8732.74 cu.cm
(iii)

10232.74 cu.cm
(iv)

12932.74 cu.cm
(v)

13732.74 cu.cm

Question 5

5.

A cone of maximum volume is carved out of a cuboid of dimensions 30.00 cm✕30.00 cm✕26.00 cm. Find the volume of the cone

(i)

5998.57 cu.cm
(ii)

6398.57 cu.cm
(iii)

6128.57 cu.cm
(iv)

6148.57 cu.cm
(v)

5908.57 cu.cm

Question 6

6.

An open cylindrical vessel of internal diameter 24.00 cm and height 22.00 cm stands on a horizontal table. Inside this is placed a solid metallic right circular cone, the diameter of whose base is 12.00 cm and height 22.00 cm and filled with water. If the cone is replaced by another cone whose height is 13.20 cm and base radius is 1.80 cm, find the drop in the water level.

(i)

9.73 cm
(ii)

1.73 cm
(iii)

2.73 cm
(iv)

0.73 cm
(v)

3.73 cm

Question 7

7.

A cylindrical vessel of base radius 19.00 cm contains water . A solid sphere of radius 15.00 cm is immersed completely in the water. Find the rise in the water level in the vessel

(i)

7.47 cm
(ii)

17.47 cm
(iii)

9.47 cm
(iv)

15.47 cm
(v)

12.47 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 4 cm. If the diameter of the beaker is 12.00 cm, find the number of marbles that are dropped in it

(i)

891
(ii)

849
(iii)

848
(iv)

864
(v)

878

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 12.00 cm and height is 24.00 cm. The radius of the hemisphere is 7.00 cm and the height of the cone is 17.00 cm. Find the volume of water left in the cylinder.

(i)

9440.38 cu.cm
(ii)

9270.38 cu.cm
(iii)

9250.38 cu.cm
(iv)

9410.38 cu.cm
(v)

9120.38 cu.cm

Question 10

10.

A conical vessel of radius 8.00 cm and height 15.00 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)

55298
120000
(ii)

55296
119998
(iii)

55296
120002
(iv)

55296
120000
(v)

55294
120000

Question 11

11.

A well of diameter 19.00 m is dug to a depth of 20.00 m and the soil from digging is evenly spread out to form a platform of base dimensions 28.00 m✕31.00 m . Find the height of the platform

(i)

5.54 m
(ii)

7.54 m
(iii)

6.54 m
(iv)

4.54 m
(v)

8.54 m

Question 12

12.

A well of diameter 17.00 m is dug to a depth of 14.00 m . The soil taken out of it has been spread evenly all around it in the shape of a circular ring of width 13m to form an embankment. Find the height of the embankment.

(i)

4.59 m
(ii)

1.59 m
(iii)

3.59 m
(iv)

0.59 m
(v)

2.59 m

Question 13

13.

An ice cream container has the shape of a right circular cylinder having inner diameter 36.00 cm and height 41.00 cm . The ice cream is filled into cones of diameter 15.00 cm and height 11.00 cm , having a hemispherical shape on the top. Find the number of such complete cones which can be filled with ice cream

(i)

27
(ii)

24
(iii)

22
(iv)

30
(v)

32

Question 14

14.

Water in a canal, 19 m wide and 4 m deep is flowing with a speed of 5 kmph . How much area will it irrigate in 55 min, if 3 cm of standing water is needed ?

(i)

9811111.11 sq.m
(ii)

11011111.11 sq.m
(iii)

11611111.11 sq.m
(iv)

11911111.11 sq.m
(v)

14211111.11 sq.m

Question 15

15.

A farmer connects a pipe of internal diameter
100 cm

from a canal into a cylindrical tank in his field,

which is
20 m
in diameter and
5 m
deep.

If water flows through the pipe at the rate of
20
3

kmph
,

in how much time will the tank be filled ?

(i)

15.00 min
(ii)

13.00 min
(iii)

18.00 min
(iv)

21.00 min
(v)

23.00 min

Assignment Key