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Aptitude test > Volume and surface area
1) What is the mass of the man, if a boat of length 4m, width 1.5m floating on
a river sinks by 0.015 m when the man gets on the boat?
a) 100kg
b) 90kg
c) 80kg
d) 70kg
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ANSWER :
SOLUTION :
Volume of water displaced = 4*1.5*0.015 = 0.09m^{3}
Mass = volume of water displaced * density of water
Mass = 0.09 * 1000
Mass = 90kg
2) For a rectangular box, what is the product of the areas of the 3 adjacent
faces that meet at a point?
a) Volume of the box
b) Twice the volume of the box
c) Half of the volume of the box
d) Square of the volume of the box
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ANSWER :
SOLUTION :
The area of the 3 adjacent faces of a rectangular box of length ‘l’, breadth
‘b’, and depth ‘h’ are ‘l*b’, ‘b*h’, and ‘l*h’.
Therefore, lb*bh*lh = l^{2}b^{2}h^{2 }= (lbh) ^{2}
= square of the volume of the box.
3) Find the number of cubes of 2cm edge will be required to fill a cubical box
of 2m edge.
a) 10^{5}
b) 10^{3}
c) 10^{4}
d) 10^{6}
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ANSWER :
SOLUTION :
Volume of the box = N*volume of the cubes … (N = number of cubes)
2^{3} = N*(0.02) ^{3}
8 = N*(0.000008)
N = 10^{6}
4) What is the ratio of the volumes of a right cylinder to that of a right cone
having equal diameters?
a) 1:3
b) 3:1
c) 2:3
d) 3:2
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ANSWER :
SOLUTION :
volume of cylinder : volume of cone
pr^{2}h : 1/3 pr^{2}h = 3 : 1
