EduSahara™ Worksheet

Question 1

1.

The height of a right circular cone is 7.00 cm and the radius of its base is 3.00 cm. It is melted and recast into a right circular cone with base radius 2.10 cm. Find the new height

(i)

19.29 cm
(ii)

17.29 cm
(iii)

11.29 cm
(iv)

9.29 cm
(v)

14.29 cm

Question 2

2.

A solid metallic cylinder of base radius 9.00 cm and height 29.00 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)

6787
(ii)

7047
(iii)

6967
(iv)

7227
(v)

7277

Question 3

3.

A conical vessel, whose internal radius is 2.50 cm and height 17.00 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)

7.85 cm
(ii)

9.85 cm
(iii)

8.85 cm
(iv)

10.85 cm
(v)

6.85 cm

Question 4

4.

A hollow metallic cylindrical tube has an internal radius of 8.00 cm and height 18.00 cm. The thickness of the metal is 2.5 cm .The tube is melted to cast into a right circular cone of height 12.00 cm. Find the radius of the cone.

(i)

9.43 cm
(ii)

19.43 cm
(iii)

17.43 cm
(iv)

14.43 cm
(v)

11.43 cm

Question 5

5.

An open cylindrical vessel of internal diameter 30.00 cm and height 30.00 cm stands on a horizontal table. Inside this is placed a solid metallic right circular cone, the diameter of whose base is 15.00 cm and height 30.00 cm and filled with water. If the cone is replaced by another cone whose height is 12.00 cm and base radius is 2.25 cm, find the drop in the water level.

(i)

0.41 cm
(ii)

3.41 cm
(iii)

1.41 cm
(iv)

4.41 cm
(v)

2.41 cm

Question 6

6.

The surface area of a solid metallic sphere is 1257.14 sq.cm. It is melted and recasted into solid right circular cones of radius 6.00 cm and height 5.00 cm . Find the number of complete cones that can be made

(i)

17
(ii)

25
(iii)

19
(iv)

27
(v)

22

Question 7

7.

A hollow sphere of internal and external diameters 14.00 cm and 18.00 cm respectively is melted into a cone of base diameter 8.00 cm. Find the height of the cone

(i)

96.50 cm
(ii)

101.50 cm
(iii)

93.50 cm
(iv)

99.50 cm
(v)

91.50 cm

Question 8

8.

A cylindrical vessel of base radius 22.00 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)

23.90 cm
(ii)

15.90 cm
(iii)

18.90 cm
(iv)

21.90 cm
(v)

13.90 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 5.6 cm. If the diameter of the beaker is 5.60 cm, find the number of marbles that are dropped in it

(i)

96
(ii)

93
(iii)

91
(iv)

99
(v)

101

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 11.00 cm and height is 19.00 cm. The radius of the hemisphere is 8.00 cm and the height of the cone is 11.00 cm. Find the volume of water left in the cylinder.

(i)

5555.14 cu.cm
(ii)

5365.14 cu.cm
(iii)

5135.14 cu.cm
(iv)

5415.14 cu.cm
(v)

5485.14 cu.cm

Question 11

11.

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)

38
81
(ii)

40
79
(iii)

14
27
(iv)

40
83
(v)

40
81

Question 12

12.

A metallic sphere of radius 17.00 cm is melted to recast into the shape of a cylinder of radius 19.00 cm . Find the height of the cylinder.

(i)

18.15 cm
(ii)

23.15 cm
(iii)

15.15 cm
(iv)

21.15 cm
(v)

13.15 cm

Question 13

13.

Metallic spheres of radii 8.00 cm, 3.00 cm are melted to form a single solid sphere. Find the radius of the resulting sphere.

(i)

3
√

539

cm
(ii)

5
√

539

cm
(iii)

3
√

537

cm
(iv)

539

cm
(v)

3
√

541

cm

Question 14

14.

A well of diameter 15.00 m is dug to a depth of 17.00 m and the soil from digging is evenly spread out to form a platform of base dimensions 22.00 m✕25.00 m . Find the height of the platform

(i)

7.46 m
(ii)

5.46 m
(iii)

4.46 m
(iv)

3.46 m
(v)

6.46 m

Question 15

15.

A well of diameter 11.00 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 9m to form an embankment. Find the height of the embankment.

(i)

9.68 m
(ii)

3.68 m
(iii)

1.68 m
(iv)

2.68 m
(v)

0.68 m

Question 16

16.

An ice cream container has the shape of a right circular cylinder having inner diameter 34.00 cm and height 40.00 cm . The ice cream is filled into cones of diameter 15.00 cm and height 18.00 cm , having a hemispherical shape on the top. Find the number of such complete cones which can be filled with ice cream

(i)

21
(ii)

23
(iii)

15
(iv)

13
(v)

18

Question 17

17.

A cylinder with radius 2.00 cm and height 9.00 cm is melted to recast into a cone of height 6.75 cm. Find the radius of the cone.

(i)

5.00 cm
(ii)

2.00 cm
(iii)

6.00 cm
(iv)

3.00 cm
(v)

4.00 cm

Question 18

18.

A copper sphere having a radius of 3.00 cm is melted and drawn into a cylindrical wire of radius 0.10 cm. Calculate the length of the wire.

(i)

41.00 m
(ii)

36.00 m
(iii)

39.00 m
(iv)

33.00 m
(v)

31.00 m

Question 19

19.

A copper rod of diameter 0.60 cm and length 2.00 cm is drawn into a wire of length 11.52 m of uniform thickness. Find the thickness of the wire.

(i)

0

cm
(ii)

3
80

cm
(iii)

1
80

cm
(iv)

1
20

cm
(v)

1
40

cm

Assignment Key