EduSahara™ Worksheet

Question 1

1.

The height of a right circular cone is 12.00 cm and the radius of its base is 3.00 cm. It is melted and recast into a right circular cone with base radius 1.50 cm. Find the new height

(i)

43.00 cm
(ii)

48.00 cm
(iii)

51.00 cm
(iv)

45.00 cm
(v)

53.00 cm

Question 2

2.

A solid metallic cylinder of base radius 10.50 cm and height 23.00 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)

7747
(ii)

7427
(iii)

7627
(iv)

7557
(v)

7607

Question 3

3.

A conical vessel, whose internal radius is 12.50 cm and height 23.00 cm, is full of liquid . Its contents are emptied into a cylindrical vessel with internal radius 10.00 cm. Find the height to which the liquid rises in the cylindrical vessel.

(i)

16.98 cm
(ii)

11.98 cm
(iii)

6.98 cm
(iv)

14.98 cm
(v)

8.98 cm

Question 4

4.

A hollow metallic cylindrical tube has an internal radius of 5.50 cm and height 10.00 cm. The thickness of the metal is 2.5 cm .The tube is melted to cast into a right circular cone of height 7.00 cm. Find the radius of the cone.

(i)

12.03 cm
(ii)

7.03 cm
(iii)

15.03 cm
(iv)

9.03 cm
(v)

17.03 cm

Question 5

5.

An open cylindrical vessel of internal diameter 29.00 cm and height 11.00 cm stands on a horizontal table. Inside this is placed a solid metallic right circular cone, the diameter of whose base is 14.50 cm and height 11.00 cm and filled with water. If the cone is replaced by another cone whose height is 6.60 cm and base radius is 2.17 cm, find the drop in the water level.

(i)

7.87 cm
(ii)

1.87 cm
(iii)

8.87 cm
(iv)

0.87 cm
(v)

2.87 cm

Question 6

6.

The surface area of a solid metallic sphere is 3218.29 sq.cm. It is melted and recasted into solid right circular cones of radius 8.00 cm and height 6.40 cm . Find the number of complete cones that can be made

(i)

34
(ii)

42
(iii)

36
(iv)

39
(v)

44

Question 7

7.

A hollow sphere of internal and external diameters 24.00 cm and 28.00 cm respectively is melted into a cone of base diameter 10.00 cm. Find the height of the cone

(i)

146.56 cm
(ii)

177.56 cm
(iii)

170.56 cm
(iv)

162.56 cm
(v)

135.56 cm

Question 8

8.

A cylindrical vessel of base radius 21.00 cm contains water . A solid sphere of radius 15.00 cm is immersed completely in the water. Find the rise in the water level in the vessel

(i)

7.20 cm
(ii)

5.20 cm
(iii)

13.20 cm
(iv)

15.20 cm
(v)

10.20 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 8.4 cm. If the diameter of the beaker is 19.60 cm, find the number of marbles that are dropped in it

(i)

1704
(ii)

1634
(iii)

1934
(iv)

1784
(v)

1764

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 7.50 cm and height is 23.50 cm. The radius of the hemisphere is 5.50 cm and the height of the cone is 15.00 cm. Find the volume of water left in the cylinder.

(i)

3550.51 cu.cm
(ii)

3330.51 cu.cm
(iii)

3170.51 cu.cm
(iv)

3470.51 cu.cm
(v)

3200.51 cu.cm

Question 11

11.

A conical vessel of radius 6.00 cm and height 8.00 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)

3
10
(ii)

3
8
(iii)

1
2
(iv)

1
8
(v)

5
8

Question 12

12.

A metallic sphere of radius 14.00 cm is melted to recast into the shape of a cylinder of radius 15.00 cm . Find the height of the cylinder.

(i)

11.26 cm
(ii)

13.26 cm
(iii)

16.26 cm
(iv)

21.26 cm
(v)

19.26 cm

Question 13

13.

Metallic spheres of radii 3.00 cm, 9.00 cm, 12.00 cm are melted to form a single solid sphere. Find the radius of the resulting sphere.

(i)

3
√

2482

cm
(ii)

2484

cm
(iii)

3
√

2484

cm
(iv)

3
√

2486

cm
(v)

5
√

2484

cm

Question 14

14.

A well of diameter 17.00 m is dug to a depth of 18.00 m and the soil from digging is evenly spread out to form a platform of base dimensions 24.00 m✕30.00 m . Find the height of the platform

(i)

7.68 m
(ii)

6.68 m
(iii)

4.68 m
(iv)

5.68 m
(v)

3.68 m

Question 15

15.

A well of diameter 19.00 m is dug to a depth of 18.00 m . The soil taken out of it has been spread evenly all around it in the shape of a circular ring of width 7m to form an embankment. Find the height of the embankment.

(i)

9.93 m
(ii)

6.93 m
(iii)

10.93 m
(iv)

8.93 m
(v)

7.93 m

Question 16

16.

An ice cream container has the shape of a right circular cylinder having inner diameter 40.00 cm and height 48.00 cm . The ice cream is filled into cones of diameter 14.00 cm and height 16.00 cm , having a hemispherical shape on the top. Find the number of such complete cones which can be filled with ice cream

(i)

36
(ii)

44
(iii)

42
(iv)

39
(v)

34

Question 17

17.

A cylinder with radius 5.00 cm and height 2.00 cm is melted to recast into a cone of height 1.85 cm. Find the radius of the cone.

(i)

11.00 cm
(ii)

8.00 cm
(iii)

9.00 cm
(iv)

7.00 cm
(v)

10.00 cm

Question 18

18.

A copper sphere having a radius of 4.00 cm is melted and drawn into a cylindrical wire of radius 0.30 cm. Calculate the length of the wire.

(i)

9.48 m
(ii)

11.48 m
(iii)

8.48 m
(iv)

10.48 m
(v)

7.48 m

Question 19

19.

A copper rod of diameter 0.60 cm and length 12.00 cm is drawn into a wire of length 27.00 m of uniform thickness. Find the thickness of the wire.

(i)

3
50

cm
(ii)

2
25

cm
(iii)

0

cm
(iv)

1
50

cm
(v)

1
25

cm

Assignment Key