EduSahara™ Worksheet

Question 1

1.

A cylindrical vessel of base radius 21.00 cm contains water . A solid sphere of radius 17.00 cm is immersed completely in the water. Find the rise in the water level in the vessel

(i)

11.85 cm
(ii)

14.85 cm
(iii)

9.85 cm
(iv)

17.85 cm
(v)

19.85 cm

Question 2

2.

If the base radius of a cone is 6.00 cm and slant height is 8.49 cm, its vertical height is

(i)

6.00 cm
(ii)

5.00 cm
(iii)

7.00 cm
(iv)

8.00 cm
(v)

4.00 cm

Question 3

3.

If the T.S.A of a sphere is 314.29 sq.cm, its radius is

(i)

3.00 cm
(ii)

4.00 cm
(iii)

7.00 cm
(iv)

5.00 cm
(v)

6.00 cm

Question 4

4.

If the base radius of a cone is 8.00 cm and vertical height is 6.00 cm, its L.S.A. is

(i)

253.43 sq.cm
(ii)

225.43 sq.cm
(iii)

251.43 sq.cm
(iv)

239.43 sq.cm
(v)

274.43 sq.cm

Question 5

5.

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)

14
27
(ii)

40
81
(iii)

38
81
(iv)

40
79
(v)

40
83

Question 6

6.

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

(i)

2352
(ii)

2522
(iii)

2392
(iv)

2332
(v)

2192

Question 7

7.

If the vertical height of a cone is 9.00 cm and volume is 235.71 cu.cm, its T.S.A is

(i)

244.43 sq.cm
(ii)

255.43 sq.cm
(iii)

222.43 sq.cm
(iv)

240.43 sq.cm
(v)

224.43 sq.cm

Question 8

8.

If the base radius of a cone is 9.00 cm and volume is 594.00 cu.cm, its base area is

(i)

237.57 sq.cm
(ii)

226.57 sq.cm
(iii)

254.57 sq.cm
(iv)

262.57 sq.cm
(v)

269.57 sq.cm

Question 9

9.

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 6.00 cm and 29.00 cm respectively. The radii of the hemispherical and conical parts are the same as that of the cylindrical part. Calculate the total surface area of the solid, if the height of the conical part is 20.00 cm

(i)

1563.74 sq.cm
(ii)

1843.74 sq.cm
(iii)

1713.74 sq.cm
(iv)

1753.74 sq.cm
(v)

1593.74 sq.cm

Question 10

10.

If the base radius of a cone is 6.00 cm and T.S.A is 287.01 sq.cm, its base area is

(i)

141.14 sq.cm
(ii)

113.14 sq.cm
(iii)

126.14 sq.cm
(iv)

98.14 sq.cm
(v)

99.14 sq.cm

Question 11

11.

A solid consists of a cylinder with two hemispherical ends with length 20.00 cm and diameter 10.00 cm. Find the total surface area of the solid

(i)

942.86 sq.cm
(ii)

935.86 sq.cm
(iii)

966.86 sq.cm
(iv)

930.86 sq.cm
(v)

946.86 sq.cm

Question 12

12.

The radii of the ends of a frustum of a right circular cone 13.00 cm high are 5.50 cm and 3.50 cm. Its total surface area is

(i)

478.61 sq.cm
(ii)

528.61 sq.cm
(iii)

490.61 sq.cm
(iv)

513.61 sq.cm
(v)

505.61 sq.cm

Question 13

13.

If the base radius of a cone is 8.00 cm and vertical height is 5.00 cm, its T.S.A is

(i)

438.24 sq.cm
(ii)

426.24 sq.cm
(iii)

461.24 sq.cm
(iv)

432.24 sq.cm
(v)

455.24 sq.cm

Question 14

14.

A metallic sphere of radius 18.00 cm is melted to recast into the shape of a cylinder of radius 21.00 cm . Find the height of the cylinder.

(i)

17.63 cm
(ii)

20.63 cm
(iii)

22.63 cm
(iv)

14.63 cm
(v)

12.63 cm

Question 15

15.

A conical vessel, whose internal radius is 4.00 cm and height 5.00 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)

21.67 cm
(ii)

23.67 cm
(iii)

26.67 cm
(iv)

29.67 cm
(v)

31.67 cm

Question 16

16.

If the slant height of a cone is 7.81 cm and vertical height is 6.00 cm, its base radius is

(i)

5.00 cm
(ii)

6.00 cm
(iii)

4.00 cm
(iv)

7.00 cm
(v)

3.00 cm

Question 17

17.

If the volume of a sphere is 3054.86 cu.cm, its T.S.A is

(i)

978.29 sq.cm
(ii)

1158.29 sq.cm
(iii)

1248.29 sq.cm
(iv)

888.29 sq.cm
(v)

1018.29 sq.cm

Question 18

18.

If the slant height of a cone is 8.60 cm and L.S.A is 189.20 sq.cm, its vertical height is

(i)

5.00 cm
(ii)

4.00 cm
(iii)

7.00 cm
(iv)

3.00 cm
(v)

6.00 cm

Question 19

19.

If the base radius of a cone is 10.00 cm and volume is 1047.62 cu.cm, its T.S.A is

(i)

736.69 sq.cm
(ii)

761.69 sq.cm
(iii)

758.69 sq.cm
(iv)

782.69 sq.cm
(v)

753.69 sq.cm

Question 20

20.

A copper sphere having a radius of 9.00 cm is melted and drawn into a cylindrical wire of radius 0.70 cm. Calculate the length of the wire.

(i)

24.84 m
(ii)

16.84 m
(iii)

19.84 m
(iv)

22.84 m
(v)

14.84 m

Question 21

21.

If the L.S.A of a sphere is 2464.00 sq.cm, its radius is

(i)

14.00 cm
(ii)

9.00 cm
(iii)

11.00 cm
(iv)

19.00 cm
(v)

17.00 cm

Question 22

22.

The height of a right circular cone is 13.00 cm and the radius of its base is 10.50 cm. It is melted and recast into a right circular cone with base radius 6.30 cm. Find the new height

(i)

33.11 cm
(ii)

36.11 cm
(iii)

31.11 cm
(iv)

39.11 cm
(v)

41.11 cm

Question 23

23.

An open cylindrical vessel of internal diameter 28.00 cm and height 10.00 cm stands on a horizontal table. Inside this is placed a solid metallic right circular cone, the diameter of whose base is 14.00 cm and height 10.00 cm and filled with water. If the cone is replaced by another cone whose height is 5.00 cm and base radius is 2.10 cm, find the drop in the water level.

(i)

2.80 cm
(ii)

7.80 cm
(iii)

0.80 cm
(iv)

1.80 cm
(v)

8.80 cm

Question 24

24.

If the volume of a sphere is 5577.52 cu.cm, its radius is

(i)

14.00 cm
(ii)

11.00 cm
(iii)

6.00 cm
(iv)

8.00 cm
(v)

16.00 cm

Question 25

25.

If the base radius of a cone is 10.00 cm and L.S.A is 351.37 sq.cm, its T.S.A is

(i)

677.66 sq.cm
(ii)

652.66 sq.cm
(iii)

678.66 sq.cm
(iv)

665.66 sq.cm
(v)

650.66 sq.cm

Assignment Key