EduSahara™ Worksheet

Question 1

1.

From a solid cylinder of height 20.00 cm and base radius 7.00 cm, a conical cavity of height 10.00 cm and base radius 7.00 cm is drilled out. Find the volume of the resulting solid

(i)

2566.67 cu.cm
(ii)

2396.67 cu.cm
(iii)

2716.67 cu.cm
(iv)

2786.67 cu.cm
(v)

2526.67 cu.cm

Question 2

2.

A solid metallic cylinder of base radius 14.50 cm and height 10.00 cm is melted to form cones each of height 1.00 cm and radius 1.00 cm . Find the number of complete cones formed

(i)

6167
(ii)

6307
(iii)

6487
(iv)

6527
(v)

6077

Question 3

3.

A conical vessel, whose internal radius is 5.50 cm and height 29.00 cm, is full of liquid . Its contents are emptied into a cylindrical vessel with internal radius 3.00 cm. Find the height to which the liquid rises in the cylindrical vessel.

(i)

29.49 cm
(ii)

35.49 cm
(iii)

37.49 cm
(iv)

32.49 cm
(v)

27.49 cm

Question 4

4.

From a circular cylinder of diameter 11.00 cm and height 10.00 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)

619.81 cu.cm
(ii)

635.81 cu.cm
(iii)

608.81 cu.cm
(iv)

647.81 cu.cm
(v)

633.81 cu.cm

Question 5

5.

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

(i)

2315.24 cu.cm
(ii)

2255.24 cu.cm
(iii)

2025.24 cu.cm
(iv)

1945.24 cu.cm
(v)

2095.24 cu.cm

Question 6

6.

A cone of maximum volume is carved out of a cuboid of dimensions 22.00 cm✕22.00 cm✕5.00 cm. Find the volume of the remaining material after the cone is carved out

(i)

2016.19 cu.cm
(ii)

1806.19 cu.cm
(iii)

1536.19 cu.cm
(iv)

1626.19 cu.cm
(v)

1786.19 cu.cm

Question 7

7.

An open cylindrical vessel of internal diameter 11.00 cm and height 20.00 cm stands on a horizontal table. Inside this is placed a solid metallic right circular cone, the diameter of whose base is 5.50 cm and height 20.00 cm and filled with water. If the cone is replaced by another cone whose height is 14.00 cm and base radius is 0.82 cm, find the drop in the water level.

(i)

1.56 cm
(ii)

2.56 cm
(iii)

0.56 cm
(iv)

3.56 cm
(v)

9.56 cm

Question 8

8.

A cylindrical vessel of base radius 16.00 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)

9.12 cm
(ii)

2.12 cm
(iii)

0.12 cm
(iv)

3.12 cm
(v)

1.12 cm

Question 9

9.

Marbles of diameter 1.60 cm are dropped into a cylindrical beaker containing some water. When they are fully submerged, the water level rises by 16 cm. If the diameter of the beaker is 16.00 cm, find the number of marbles that are dropped in it

(i)

1430
(ii)

1620
(iii)

1500
(iv)

1540
(v)

1260

Question 10

10.

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 8.50 cm and the height of the cone is 15.00 cm. Find the volume of water left in the cylinder.

(i)

9282.37 cu.cm
(ii)

11282.37 cu.cm
(iii)

10682.37 cu.cm
(iv)

12582.37 cu.cm
(v)

11082.37 cu.cm

Question 11

11.

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 7.50 cm and 31.50 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 20.00 cm

(i)

7651.25 cu.cm
(ii)

7781.25 cu.cm
(iii)

7511.25 cu.cm
(iv)

7491.25 cu.cm
(v)

7631.25 cu.cm

Question 12

12.

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)

14
27
(iii)

40
81
(iv)

38
81
(v)

40
79

Question 13

13.

A well of diameter 17.00 m is dug to a depth of 16.00 m and the soil from digging is evenly spread out to form a platform of base dimensions 21.00 m✕25.00 m . Find the height of the platform

(i)

5.92 m
(ii)

8.92 m
(iii)

4.92 m
(iv)

6.92 m
(v)

7.92 m

Question 14

14.

A well of diameter 19.00 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 12m to form an embankment. Find the height of the embankment.

(i)

5.61 m
(ii)

4.61 m
(iii)

3.61 m
(iv)

6.61 m
(v)

2.61 m

Question 15

15.

An ice cream container has the shape of a right circular cylinder having inner diameter 30.00 cm and height 32.00 cm . The ice cream is filled into cones of diameter 10.00 cm and height 10.00 cm , having a hemispherical shape on the top. Find the number of such complete cones which can be filled with ice cream

(i)

40
(ii)

48
(iii)

38
(iv)

43
(v)

46

Question 16

16.

Water in a canal, 20 m wide and 3 m deep is flowing with a speed of 13 kmph . How much area will it irrigate in 30 min, if 8 cm of standing water is needed ?

(i)

4755000.00 sq.m
(ii)

5155000.00 sq.m
(iii)

4925000.00 sq.m
(iv)

4615000.00 sq.m
(v)

4875000.00 sq.m

Question 17

17.

A farmer connects a pipe of internal diameter
56 cm

from a canal into a cylindrical tank in his field,

which is
14 m
in diameter and
4 m
deep.

If water flows through the pipe at the rate of
25
6

kmph
,

in how much time will the tank be filled ?

(i)

36.00 min
(ii)

33.00 min
(iii)

39.00 min
(iv)

31.00 min
(v)

41.00 min

Assignment Key