EduSahara™ Worksheet

Question 1

1.

The height of a right circular cone is 19.00 cm and the radius of its base is 4.00 cm. It is melted and recast into a right circular cone with base radius 2.80 cm. Find the new height

(i)

33.78 cm
(ii)

41.78 cm
(iii)

38.78 cm
(iv)

35.78 cm
(v)

43.78 cm

Question 2

2.

A solid metallic cylinder of base radius 9.00 cm and height 8.00 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)

1764
(ii)

1724
(iii)

1944
(iv)

2084
(v)

1994

Question 3

3.

A conical vessel, whose internal radius is 9.50 cm and height 5.00 cm, is full of liquid . Its contents are emptied into a cylindrical vessel with internal radius 5.00 cm. Find the height to which the liquid rises in the cylindrical vessel.

(i)

5.02 cm
(ii)

8.02 cm
(iii)

7.02 cm
(iv)

4.02 cm
(v)

6.02 cm

Question 4

4.

A hollow metallic cylindrical tube has an internal radius of 13.00 cm and height 11.00 cm. The thickness of the metal is 4.5 cm .The tube is melted to cast into a right circular cone of height 6.00 cm. Find the radius of the cone.

(i)

22.47 cm
(ii)

24.47 cm
(iii)

32.47 cm
(iv)

30.47 cm
(v)

27.47 cm

Question 5

5.

An open cylindrical vessel of internal diameter 19.00 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 9.50 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 1.43 cm, find the drop in the water level.

(i)

0.81 cm
(ii)

9.81 cm
(iii)

1.81 cm
(iv)

3.81 cm
(v)

2.81 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 10.00 cm . Find the number of complete cones that can be made

(i)

44
(ii)

49
(iii)

46
(iv)

54
(v)

52

Question 7

7.

A hollow sphere of internal and external diameters 12.00 cm and 18.00 cm respectively is melted into a cone of base diameter 4.00 cm. Find the height of the cone

(i)

526.00 cm
(ii)

513.00 cm
(iii)

505.00 cm
(iv)

538.00 cm
(v)

497.00 cm

Question 8

8.

A cylindrical vessel of base radius 10.00 cm contains water . A solid sphere of radius 7.00 cm is immersed completely in the water. Find the rise in the water level in the vessel

(i)

6.57 cm
(ii)

2.57 cm
(iii)

3.57 cm
(iv)

4.57 cm
(v)

5.57 cm

Question 9

9.

Marbles of diameter 1.40 cm are dropped into a cylindrical beaker containing some water. When they are fully submerged, the water level rises by 14 cm. If the diameter of the beaker is 19.60 cm, find the number of marbles that are dropped in it

(i)

2940
(ii)

3110
(iii)

2710
(iv)

3090
(v)

2760

Question 10

10.

A metallic sphere of radius 20.00 cm is melted to recast into the shape of a cylinder of radius 24.00 cm . Find the height of the cylinder.

(i)

23.52 cm
(ii)

21.52 cm
(iii)

13.52 cm
(iv)

15.52 cm
(v)

18.52 cm

Question 11

11.

Metallic spheres of radii 12.00 cm, 3.00 cm are melted to form a single solid sphere. Find the radius of the resulting sphere.

(i)

5
√

1755

cm
(ii)

3
√

1755

cm
(iii)

3
√

1752

cm
(iv)

3
√

1758

cm
(v)

1755

cm

Question 12

12.

A well of diameter 19.00 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 21.00 m✕34.00 m . Find the height of the platform

(i)

8.55 m
(ii)

9.55 m
(iii)

6.55 m
(iv)

5.55 m
(v)

7.55 m

Question 13

13.

A well of diameter 14.00 m is dug to a depth of 20.00 m . The soil taken out of it has been spread evenly all around it in the shape of a circular ring of width 9m to form an embankment. Find the height of the embankment.

(i)

5.73 m
(ii)

6.73 m
(iii)

3.73 m
(iv)

2.73 m
(v)

4.73 m

Question 14

14.

An ice cream container has the shape of a right circular cylinder having inner diameter 30.00 cm and height 34.00 cm . The ice cream is filled into cones of diameter 10.00 cm and height 20.00 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)

35
(iii)

33
(iv)

25
(v)

30

Question 15

15.

A cylinder with radius 1.00 cm and height 9.00 cm is melted to recast into a cone of height 0.75 cm. Find the radius of the cone.

(i)

6.00 cm
(ii)

7.00 cm
(iii)

4.00 cm
(iv)

5.00 cm
(v)

8.00 cm

Question 16

16.

A copper sphere having a radius of 6.00 cm is melted and drawn into a cylindrical wire of radius 0.90 cm. Calculate the length of the wire.

(i)

5.56 m
(ii)

1.56 m
(iii)

2.56 m
(iv)

3.56 m
(v)

4.56 m

Question 17

17.

A copper rod of diameter 1.00 cm and length 4.00 cm is drawn into a wire of length 4.00 m of uniform thickness. Find the thickness of the wire.

(i)

1
10

cm
(ii)

1
5

cm
(iii)

1
20

cm
(iv)

3
20

cm
(v)

0

cm

Question 18

18.

Water in a canal, 11 m wide and 3 m deep is flowing with a speed of 12 kmph . How much area will it irrigate in 40 min, if 7 cm of standing water is needed ?

(i)

3921428.57 sq.m
(ii)

3771428.57 sq.m
(iii)

3811428.57 sq.m
(iv)

3591428.57 sq.m
(v)

3601428.57 sq.m

Question 19

19.

A farmer connects a pipe of internal diameter
70 cm

from a canal into a cylindrical tank in his field,

which is
14 m
in diameter and
5 m
deep.

If water flows through the pipe at the rate of
20
11

kmph
,

in how much time will the tank be filled ?

(i)

61.00 min
(ii)

63.00 min
(iii)

69.00 min
(iv)

66.00 min
(v)

71.00 min

Assignment Key