EduSahara™ Worksheet

Question 1

1.

A copper rod of diameter 1.00 cm and length 14.00 cm is drawn into a wire of length 350.00 m of uniform thickness. Find the thickness of the wire.

(i)

1
100

cm
(ii)

1
50

cm
(iii)

3
100

cm
(iv)

1
25

cm
(v)

0

cm

Question 2

2.

If the slant height of a cone is 11.18 cm and vertical height is 5.00 cm, its volume is

(i)

519.81 cu.cm
(ii)

523.81 cu.cm
(iii)

540.81 cu.cm
(iv)

529.81 cu.cm
(v)

511.81 cu.cm

Question 3

3.

If the slant height of a cone is 14.14 cm and vertical height is 10.00 cm, its L.S.A. is

(i)

444.40 sq.cm
(ii)

417.40 sq.cm
(iii)

458.40 sq.cm
(iv)

456.40 sq.cm
(v)

436.40 sq.cm

Question 4

4.

If the vertical height of a cone is 6.00 cm and volume is 402.29 cu.cm, its T.S.A is

(i)

467.57 sq.cm
(ii)

435.57 sq.cm
(iii)

452.57 sq.cm
(iv)

480.57 sq.cm

Question 5

5.

A cone of maximum volume is carved out of a cuboid of dimensions 19.00 cm✕19.00 cm✕30.00 cm. Find the volume of the cone

(i)

2566.43 cu.cm
(ii)

2816.43 cu.cm
(iii)

2996.43 cu.cm
(iv)

2836.43 cu.cm
(v)

3086.43 cu.cm

Question 6

6.

If the base radius of a cone is 10.00 cm and slant height is 12.81 cm, its vertical height is

(i)

10.00 cm
(ii)

8.00 cm
(iii)

9.00 cm
(iv)

6.00 cm
(v)

7.00 cm

Question 7

7.

The surface area of a solid metallic sphere is 9164.57 sq.cm. It is melted and recasted into solid right circular cones of radius 10.80 cm and height 10.80 cm . Find the number of complete cones that can be made

(i)

57
(ii)

59
(iii)

62
(iv)

67
(v)

65

Question 8

8.

A cylinder with radius 4.00 cm and height 1.00 cm is melted to recast into a cone of height 12.00 cm. Find the radius of the cone.

(i)

0.00 cm
(ii)

4.00 cm
(iii)

1.00 cm
(iv)

2.00 cm
(v)

3.00 cm

Question 9

9.

If the volume of a sphere is 24438.86 cu.cm, its L.S.A is

(i)

4343.14 sq.cm
(ii)

4123.14 sq.cm
(iii)

3953.14 sq.cm
(iv)

4073.14 sq.cm
(v)

3933.14 sq.cm

Question 10

10.

The height of a right circular cone is 18.00 cm and the radius of its base is 2.50 cm. It is melted and recast into a right circular cone with base radius 2.00 cm. Find the new height

(i)

28.12 cm
(ii)

25.12 cm
(iii)

31.12 cm
(iv)

33.12 cm
(v)

23.12 cm

Question 11

11.

Two cubes each of volume 4913.00 cu.cm are joined end to end . Find the surface area of the resulting cuboid.

(i)

2770.00 sq.cm
(ii)

2890.00 sq.cm
(iii)

2950.00 sq.cm
(iv)

2630.00 sq.cm
(v)

3120.00 sq.cm

Question 12

12.

If the base radius of a cone is 9.00 cm and T.S.A is 635.01 sq.cm, its L.S.A. is

(i)

380.44 sq.cm
(ii)

408.44 sq.cm
(iii)

375.44 sq.cm
(iv)

387.44 sq.cm
(v)

354.44 sq.cm

Question 13

13.

If the vertical height of a cone is 7.00 cm and volume is 733.33 cu.cm, its base radius is

(i)

15.00 cm
(ii)

7.00 cm
(iii)

5.00 cm
(iv)

13.00 cm
(v)

10.00 cm

Question 14

14.

A hollow sphere of internal and external diameters 16.00 cm and 22.00 cm respectively is melted into a cone of base diameter 12.00 cm. Find the height of the cone

(i)

88.00 cm
(ii)

86.00 cm
(iii)

91.00 cm
(iv)

96.00 cm
(v)

94.00 cm

Question 15

15.

A solid consists of a right circular cylinder with a hemisphere on one end and a cone on the other . The radius and height of the cylindrical part are 5.00 cm and 19.00 cm respectively. The radii of the hemispherical and conical parts are the same as that of the cylindrical part. Calculate the volume of the solid, if the height of the conical part is 12.00 cm

(i)

2219.05 cu.cm
(ii)

2209.05 cu.cm
(iii)

2069.05 cu.cm
(iv)

2039.05 cu.cm
(v)

1889.05 cu.cm

Question 16

16.

If the L.S.A of a sphere is 3633.14 sq.cm, its radius is

(i)

14.00 cm
(ii)

17.00 cm
(iii)

12.00 cm
(iv)

20.00 cm
(v)

22.00 cm

Question 17

17.

The radii of the ends of a frustum of a right circular cone 9.00 cm high are 7.50 cm and 4.50 cm. Its volume is

(i)

1319.50 cu.cm
(ii)

1039.50 cu.cm
(iii)

1079.50 cu.cm
(iv)

799.50 cu.cm
(v)

909.50 cu.cm

Question 18

18.

A metallic sphere of radius 20.00 cm is melted to recast into the shape of a cylinder of radius 23.00 cm . Find the height of the cylinder.

(i)

17.16 cm
(ii)

20.16 cm
(iii)

23.16 cm
(iv)

15.16 cm
(v)

25.16 cm

Question 19

19.

If the base radius of a cone is 9.00 cm and L.S.A is 380.44 sq.cm, its slant height is

(i)

8.45 cm
(ii)

13.45 cm
(iii)

18.45 cm
(iv)

10.45 cm
(v)

16.45 cm

Question 20

20.

A solid consists of a cylinder with two hemispherical ends with length 35.00 cm and diameter 15.00 cm. Find the total surface area of the solid

(i)

2187.14 sq.cm
(ii)

2357.14 sq.cm
(iii)

2397.14 sq.cm
(iv)

2587.14 sq.cm
(v)

2107.14 sq.cm

Question 21

21.

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)

5
8
(ii)

1
2
(iii)

1
8
(iv)

3
8
(v)

3
10

Question 22

22.

If the base radius of a cone is 6.00 cm and L.S.A is 188.57 sq.cm, its volume is

(i)

315.71 cu.cm
(ii)

279.71 cu.cm
(iii)

285.71 cu.cm
(iv)

328.71 cu.cm
(v)

301.71 cu.cm

Question 23

23.

An ice cream container has the shape of a right circular cylinder having inner diameter 32.00 cm and height 37.00 cm . The ice cream is filled into cones of diameter 11.00 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)

35
(ii)

37
(iii)

32
(iv)

29
(v)

27

Question 24

24.

A hollow metallic cylindrical tube has an internal radius of 14.00 cm and height 16.00 cm. The thickness of the metal is 2.5 cm .The tube is melted to cast into a right circular cone of height 6.00 cm. Find the radius of the cone.

(i)

27.70 cm
(ii)

24.70 cm
(iii)

29.70 cm
(iv)

19.70 cm
(v)

21.70 cm

Question 25

25.

If the slant height of a cone is 12.04 cm and L.S.A is 302.72 sq.cm, its T.S.A is

(i)

508.86 sq.cm
(ii)

503.86 sq.cm
(iii)

500.86 sq.cm
(iv)

521.86 sq.cm
(v)

480.86 sq.cm

Assignment Key