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Q.

The surface area of the six faces of a rectangular solid are 16,16,32,32,72 and 72 cm2. The volume of the solid (in cm) is


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a

200cm3

b

192cm3

c

250cm3

d

225cm3 

answer is B.

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Detailed Solution

It is given surface area of the six faces of a rectangular solid are 16,16,32,32,72 and 72 cm2.
Let the dimensions of boxes be L, B and H.
So, Surface area of each face of 6 faces is LB , LB , BH , BH , LH and LH.
Thus, we can write the values of dimensions as,
LB=16 BH=32 LH=72  
Multiplying vertically, we get,
(LB)(BH)(LH)=(16)(32)(72) (LBH) 2 =(16)(16×2)( 6 2 ×2) (LBH) 2 = (16×6×2) 2 LBH=192  
As LBH = volume of cuboid.
So, volume of cuboid = 192 cm³.
Therefore, the correct option is 2.
 
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