EduSahara™ Worksheet

Question 1

1.

From a solid cylinder of height 17.00 cm and base radius 9.50 cm, a conical cavity of height 5.00 cm and base radius 9.50 cm is drilled out. Find the volume of the resulting solid

(i)

4349.19 cu.cm
(ii)

4129.19 cu.cm
(iii)

4309.19 cu.cm
(iv)

4479.19 cu.cm
(v)

4499.19 cu.cm

Question 2

2.

A conical vessel, whose internal radius is 3.50 cm and height 15.00 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)

12.31 cm
(ii)

15.31 cm
(iii)

10.31 cm
(iv)

18.31 cm
(v)

20.31 cm

Question 3

3.

From a circular cylinder of diameter 20.00 cm and height 16.00 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)

3382.38 cu.cm
(ii)

3352.38 cu.cm
(iii)

3192.38 cu.cm
(iv)

3532.38 cu.cm
(v)

3282.38 cu.cm

Question 4

4.

A cone of maximum volume is carved out of a cube of edge 6.00 cm. Find the volume of the cone

(i)

61.57 cu.cm
(ii)

56.57 cu.cm
(iii)

53.57 cu.cm
(iv)

59.57 cu.cm
(v)

51.57 cu.cm

Question 5

5.

A cone of maximum volume is carved out of a cuboid of dimensions 5.00 cm✕5.00 cm✕9.00 cm. Find the volume of the cone

(i)

63.93 cu.cm
(ii)

55.93 cu.cm
(iii)

53.93 cu.cm
(iv)

61.93 cu.cm
(v)

58.93 cu.cm

Question 6

6.

An open cylindrical vessel of internal diameter 20.00 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 10.00 cm and height 23.00 cm and filled with water. If the cone is replaced by another cone whose height is 13.80 cm and base radius is 3.00 cm, find the drop in the water level.

(i)

0.50 cm
(ii)

9.50 cm
(iii)

3.50 cm
(iv)

2.50 cm
(v)

1.50 cm

Question 7

7.

A cylindrical vessel of base radius 10.00 cm contains water . A solid sphere of radius 6.00 cm is immersed completely in the water. Find the rise in the water level in the vessel

(i)

3.88 cm
(ii)

0.88 cm
(iii)

2.88 cm
(iv)

1.88 cm
(v)

4.88 cm

Question 8

8.

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 10.50 cm and height is 28.50 cm. The radius of the hemisphere is 5.50 cm and the height of the cone is 19.00 cm. Find the volume of water left in the cylinder.

(i)

8784.54 cu.cm
(ii)

9164.54 cu.cm
(iii)

8924.54 cu.cm
(iv)

8844.54 cu.cm
(v)

8994.54 cu.cm

Question 9

9.

A solid consists of a right circular cylinder with a hemisphere on one end and a cone on the other . The radius and height of the cylindrical part are 6.00 cm and 26.00 cm respectively. The radii of the hemispherical and conical parts are the same as that of the cylindrical part. Calculate the volume of the solid, if the height of the conical part is 18.00 cm

(i)

4223.14 cu.cm
(ii)

4073.14 cu.cm
(iii)

3913.14 cu.cm
(iv)

3793.14 cu.cm
(v)

4143.14 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)

1
8
(ii)

1
2
(iii)

5
8
(iv)

3
10
(v)

3
8

Question 11

11.

Water in a canal, 9 m wide and 5 m deep is flowing with a speed of 10 kmph . How much area will it irrigate in 35 min, if 9 cm of standing water is needed ?

(i)

3156666.67 sq.m
(ii)

2756666.67 sq.m
(iii)

2916666.67 sq.m
(iv)

2666666.67 sq.m
(v)

2946666.67 sq.m

Question 12

12.

A farmer connects a pipe of internal diameter
28 cm

from a canal into a cylindrical tank in his field,

which is
14 m
in diameter and
2 m
deep.

If water flows through the pipe at the rate of
25
4

kmph
,

in how much time will the tank be filled ?

(i)

53.00 min
(ii)

43.00 min
(iii)

45.00 min
(iv)

48.00 min
(v)

51.00 min

Assignment Key