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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

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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
$10 square root of 2$
$5 square root of 3$

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.

50

150

250

350

150

Let x be no of spherical marbles put into the cylindrical beaker.
Now,
Volume of one marble = $4 over 3 πr cubed$
$equals space 4 over 3 straight pi open parentheses fraction numerator 1.4 over denominator 2 end fraction close parentheses cubed$
Volume of x marbles = $straight x space cross times space open parentheses fraction numerator 1.4 over denominator 2 end fraction close parentheses cubed$
Volume of water increased in the cylindrical beaker = $straight pi space cross times space open parentheses 7 over 2 close parentheses squared space cross times space 5.6$

According to the question,
Volume of x marbles = Volume of water increased in the cylindrical beaker
$rightwards double arrow space space 4 over 3 space cross times space 0.7 space cross times space 0.7 space cross times space straight x space equals space 3.5 space cross times space 3.5 space cross times space 5.6 rightwards double arrow space space space space space space straight x space equals space fraction numerator 3.5 space cross times space 3.5 space cross times space 5.6 space cross times space 3 over denominator 4 space cross times space 0.7 space cross times space 0.7 space cross times 0.7 end fraction space equals space 150$

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