EduSahara™ Worksheet

Question 1

1.

The height of a right circular cone is 20.00 cm and the radius of its base is 12.50 cm. It is melted and recast into a right circular cone with base radius 10.00 cm. Find the new height

(i)

36.25 cm
(ii)

26.25 cm
(iii)

28.25 cm
(iv)

31.25 cm
(v)

34.25 cm

Question 2

2.

A solid metallic cylinder of base radius 7.00 cm and height 15.00 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)

2125
(ii)

2435
(iii)

2265
(iv)

2205
(v)

2055

Question 3

3.

A conical vessel, whose internal radius is 6.50 cm and height 12.00 cm, is full of liquid . Its contents are emptied into a cylindrical vessel with internal radius 1.00 cm. Find the height to which the liquid rises in the cylindrical vessel.

(i)

155.00 cm
(ii)

172.00 cm
(iii)

169.00 cm
(iv)

191.00 cm
(v)

164.00 cm

Question 4

4.

A hollow metallic cylindrical tube has an internal radius of 6.50 cm and height 24.00 cm. The thickness of the metal is 3 cm .The tube is melted to cast into a right circular cone of height 16.00 cm. Find the radius of the cone.

(i)

11.70 cm
(ii)

17.70 cm
(iii)

19.70 cm
(iv)

14.70 cm
(v)

9.70 cm

Question 5

5.

An open cylindrical vessel of internal diameter 20.00 cm and height 18.00 cm stands on a horizontal table. Inside this is placed a solid metallic right circular cone, the diameter of whose base is 10.00 cm and height 18.00 cm and filled with water. If the cone is replaced by another cone whose height is 9.00 cm and base radius is 3.50 cm, find the drop in the water level.

(i)

1.13 cm
(ii)

9.13 cm
(iii)

3.13 cm
(iv)

0.13 cm
(v)

2.13 cm

Question 6

6.

The surface area of a solid metallic sphere is 4538.29 sq.cm. It is melted and recasted into solid right circular cones of radius 9.50 cm and height 5.70 cm . Find the number of complete cones that can be made

(i)

56
(ii)

50
(iii)

58
(iv)

53
(v)

48

Question 7

7.

A hollow sphere of internal and external diameters 40.00 cm and 44.00 cm respectively is melted into a cone of base diameter 12.00 cm. Find the height of the cone

(i)

294.22 cm
(ii)

302.22 cm
(iii)

276.22 cm
(iv)

319.22 cm
(v)

278.22 cm

Question 8

8.

A cylindrical vessel of base radius 16.00 cm contains water . A solid sphere of radius 12.00 cm is immersed completely in the water. Find the rise in the water level in the vessel

(i)

11.00 cm
(ii)

9.00 cm
(iii)

8.00 cm
(iv)

10.00 cm
(v)

7.00 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 8.40 cm, find the number of marbles that are dropped in it

(i)

234
(ii)

216
(iii)

232
(iv)

199
(v)

191

Question 10

10.

A metallic sphere of radius 18.00 cm is melted to recast into the shape of a cylinder of radius 20.00 cm . Find the height of the cylinder.

(i)

24.44 cm
(ii)

16.44 cm
(iii)

22.44 cm
(iv)

14.44 cm
(v)

19.44 cm

Question 11

11.

Metallic spheres of radii 10.00 cm, 14.00 cm, 5.00 cm are melted to form a single solid sphere. Find the radius of the resulting sphere.

(i)

3
√

3872

cm
(ii)

3
√

3867

cm
(iii)

3869

cm
(iv)

5
√

3869

cm
(v)

3
√

3869

cm

Question 12

12.

A well of diameter 18.00 m is dug to a depth of 20.00 m and the soil from digging is evenly spread out to form a platform of base dimensions 24.00 m✕27.00 m . Find the height of the platform

(i)

8.86 m
(ii)

6.86 m
(iii)

9.86 m
(iv)

7.86 m
(v)

5.86 m

Question 13

13.

A well of diameter 10.00 m is dug to a depth of 15.00 m . The soil taken out of it has been spread evenly all around it in the shape of a circular ring of width 14m to form an embankment. Find the height of the embankment.

(i)

3.12 m
(ii)

0.12 m
(iii)

2.12 m
(iv)

9.12 m
(v)

1.12 m

Question 14

14.

An ice cream container has the shape of a right circular cylinder having inner diameter 26.00 cm and height 30.00 cm . The ice cream is filled into cones of diameter 20.00 cm and height 15.00 cm , having a hemispherical shape on the top. Find the number of such complete cones which can be filled with ice cream

(i)

2
(ii)

4
(iii)

3
(iv)

5
(v)

6

Question 15

15.

A cylinder with radius 3.00 cm and height 2.00 cm is melted to recast into a cone of height 1.10 cm. Find the radius of the cone.

(i)

6.00 cm
(ii)

8.00 cm
(iii)

9.00 cm
(iv)

5.00 cm
(v)

7.00 cm

Question 16

16.

A copper sphere having a radius of 9.00 cm is melted and drawn into a cylindrical wire of radius 0.10 cm. Calculate the length of the wire.

(i)

989.00 m
(ii)

946.00 m
(iii)

964.00 m
(iv)

978.00 m
(v)

972.00 m

Question 17

17.

A copper rod of diameter 1.00 cm and length 2.00 cm is drawn into a wire of length 18.00 m of uniform thickness. Find the thickness of the wire.

(i)

1
30

cm
(ii)

1
20

cm
(iii)

1
15

cm
(iv)

1
60

cm
(v)

0

cm

Question 18

18.

Water in a canal, 18 m wide and 5 m deep is flowing with a speed of 19 kmph . How much area will it irrigate in 10 min, if 4 cm of standing water is needed ?

(i)

7005000.00 sq.m
(ii)

6995000.00 sq.m
(iii)

7125000.00 sq.m
(iv)

7265000.00 sq.m

Question 19

19.

A farmer connects a pipe of internal diameter
4 cm

from a canal into a cylindrical tank in his field,

which is
4 m
in diameter and
1 m
deep.

If water flows through the pipe at the rate of
20

kmph
,

in how much time will the tank be filled ?

(i)

30.00 min
(ii)

33.00 min
(iii)

25.00 min
(iv)

35.00 min
(v)

27.00 min

Assignment Key