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Mensuration - Volume and Surface Areas

Multiple Choice Questions

101.

The heights of a cone and a cylinder are equal. The radii of their bases are in the ratio 2 : 1. The ratio of their volume is

4 : 3
3 : 4
2 : 1
1 : 2

59 Views

102.

A spherical lead ball of radius 6 cm is melted and small lead balls of radius 3 mm are made. The total number of possible small lead balls is:

4250
4000
8005
8000

80 Views

103.

If $4 straight r space equals space straight h space plus space square root of straight r squared plus straight h squared end root$ then r : h is $left parenthesis straight r not equal to 0 right parenthesis$

17 : 8
8 : 17
8 : 15
15 : 8

104.
The length (in metres) of the longest rod that can be put in a room of dimensions 10 m x 10 m x 5 m is

$15 square root of 3$

15

$10 square root of 2$

$5 square root of 3$

The length of the longest rod shall be equal to the diagonal of the room
$Diagonal space equals space square root of straight l squared space plus space straight b squared space plus space straight h squared end root$
Hence, length of the rod
$equals space square root of left parenthesis 10 right parenthesis squared space plus space left parenthesis 10 right parenthesis squared space plus space left parenthesis 5 right parenthesis squared end root equals space square root of 100 space plus space 100 space plus space 25 end root equals space square root of 225 space equals space 15 space straight m$

41 Views

105.

The volume (in m³) of rain water that can be collected from 1.5 hect of ground in a rainfall of 5 cm is

75
750
7500
75000

36 Views

106.

A river 3 m deep and 40 m wide is flowing at the rate of 2 km/h. How much water (in litres) will fall into the sea in a minute?

400000
4000000
40000
4000

37 Views

107.

A hemisphere and a cone have equal bases. If their heights are also equal, the ratio of their curved surfaces will be

$1 space colon square root of 2$
$square root of 2 space colon space 1$
1 : 2
2 : 1

55 Views

108.

Marbles of diameter 1.4 cm are dropped into a cylindrical beaker containing some water and are fully submerged. The diameter of the beaker is 7 cm. Find how many marbles have been dropped in it, if the water rises by 5.6 cm.

30 Views

109.

Water is flowing at the rate of 3 km/h through a circular pipe of 20 cm internal diameter into a circular cistern of diameter 10 m and depth 2 m. In how much time will the cistern be filled?

1 h
1 h 40 min
1 h 20 min
2 h 40 min

33 Views

110.

The total surface area of a sphere is $8 straight pi$ square unit. The volume of the sphere is

$8 divided by 3 space straight pi$ cu unit.
$8 square root of 3 space straight pi space cu space unit$
$fraction numerator 8 square root of 3 over denominator 5 end fraction straight pi space cu space unit$
$fraction numerator 8 square root of 2 over denominator 3 end fraction straight pi space cu space unit$