EduSahara™ Worksheet

Question 1

1.

The height of a right circular cone is 7.00 cm and the radius of its base is 13.50 cm. It is melted and recast into a right circular cone with base radius 10.80 cm. Find the new height

(i)

5.94 cm
(ii)

10.94 cm
(iii)

7.94 cm
(iv)

13.94 cm
(v)

15.94 cm

Question 2

2.

A solid metallic cylinder of base radius 4.50 cm and height 20.00 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)

1045
(ii)

1155
(iii)

1235
(iv)

1215
(v)

1485

Question 3

3.

A conical vessel, whose internal radius is 11.50 cm and height 23.00 cm, is full of liquid . Its contents are emptied into a cylindrical vessel with internal radius 4.00 cm. Find the height to which the liquid rises in the cylindrical vessel.

(i)

63.37 cm
(ii)

66.37 cm
(iii)

58.37 cm
(iv)

68.37 cm
(v)

60.37 cm

Question 4

4.

A hollow metallic cylindrical tube has an internal radius of 9.00 cm and height 14.00 cm. The thickness of the metal is 2 cm .The tube is melted to cast into a right circular cone of height 9.00 cm. Find the radius of the cone.

(i)

13.66 cm
(ii)

18.66 cm
(iii)

10.66 cm
(iv)

8.66 cm
(v)

16.66 cm

Question 5

5.

An open cylindrical vessel of internal diameter 27.00 cm and height 24.00 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 24.00 cm and filled with water. If the cone is replaced by another cone whose height is 12.00 cm and base radius is 3.38 cm, find the drop in the water level.

(i)

0.75 cm
(ii)

3.75 cm
(iii)

9.75 cm
(iv)

1.75 cm
(v)

2.75 cm

Question 6

6.

The surface area of a solid metallic sphere is 5028.57 sq.cm. It is melted and recasted into solid right circular cones of radius 8.00 cm and height 14.00 cm . Find the number of complete cones that can be made

(i)

38
(ii)

40
(iii)

30
(iv)

35
(v)

32

Question 7

7.

A hollow sphere of internal and external diameters 36.00 cm and 42.00 cm respectively is melted into a cone of base diameter 26.00 cm. Find the height of the cone

(i)

78.16 cm
(ii)

86.16 cm
(iii)

81.16 cm
(iv)

76.16 cm
(v)

84.16 cm

Question 8

8.

A cylindrical vessel of base radius 29.00 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)

10.87 cm
(ii)

13.87 cm
(iii)

5.87 cm
(iv)

15.87 cm
(v)

7.87 cm

Question 9

9.

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)

4860
(ii)

4710
(iii)

4940
(iv)

4980
(v)

4630

Question 10

10.

A metallic sphere of radius 13.00 cm is melted to recast into the shape of a cylinder of radius 16.00 cm . Find the height of the cylinder.

(i)

14.44 cm
(ii)

8.44 cm
(iii)

16.44 cm
(iv)

6.44 cm
(v)

11.44 cm

Question 11

11.

Metallic spheres of radii 9.00 cm, 11.00 cm are melted to form a single solid sphere. Find the radius of the resulting sphere.

(i)

3
√

2058

cm
(ii)

2060

cm
(iii)

3
√

2062

cm
(iv)

5
√

2060

cm
(v)

3
√

2060

cm

Question 12

12.

A well of diameter 19.00 m is dug to a depth of 11.00 m and the soil from digging is evenly spread out to form a platform of base dimensions 17.00 m✕31.00 m . Find the height of the platform

(i)

5.92 m
(ii)

3.92 m
(iii)

4.92 m
(iv)

7.92 m
(v)

6.92 m

Question 13

13.

A well of diameter 15.00 m is dug to a depth of 10.00 m . The soil taken out of it has been spread evenly all around it in the shape of a circular ring of width 6m to form an embankment. Find the height of the embankment.

(i)

6.46 m
(ii)

4.46 m
(iii)

2.46 m
(iv)

5.46 m
(v)

3.46 m

Question 14

14.

An ice cream container has the shape of a right circular cylinder having inner diameter 30.00 cm and height 40.00 cm . The ice cream is filled into cones of diameter 13.00 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)

29
(ii)

31
(iii)

26
(iv)

23
(v)

21

Question 15

15.

A cylinder with radius 10.00 cm and height 3.00 cm is melted to recast into a cone of height 900.00 cm. Find the radius of the cone.

(i)

0.00 cm
(ii)

2.00 cm
(iii)

9.00 cm
(iv)

1.00 cm
(v)

3.00 cm

Question 16

16.

A copper sphere having a radius of 5.00 cm is melted and drawn into a cylindrical wire of radius 0.20 cm. Calculate the length of the wire.

(i)

44.67 m
(ii)

41.67 m
(iii)

46.67 m
(iv)

36.67 m
(v)

38.67 m

Question 17

17.

A copper rod of diameter 1.40 cm and length 6.00 cm is drawn into a wire of length 47.04 m of uniform thickness. Find the thickness of the wire.

(i)

1
20

cm
(ii)

1
10

cm
(iii)

1
40

cm
(iv)

3
40

cm
(v)

0

cm

Question 18

18.

Water in a canal, 8 m wide and 5 m deep is flowing with a speed of 7 kmph . How much area will it irrigate in 55 min, if 7 cm of standing water is needed ?

(i)

3406666.67 sq.m
(ii)

3666666.67 sq.m
(iii)

3646666.67 sq.m
(iv)

3806666.67 sq.m
(v)

3816666.67 sq.m

Question 19

19.

A farmer connects a pipe of internal diameter
18 cm

from a canal into a cylindrical tank in his field,

which is
18 m
in diameter and
1 m
deep.

If water flows through the pipe at the rate of
25

kmph
,

in how much time will the tank be filled ?

(i)

27.00 min
(ii)

21.00 min
(iii)

29.00 min
(iv)

19.00 min
(v)

24.00 min

Assignment Key