Question

The surface areas of the six faces of a rectangular solid are $16,16,32,32,72$and $72$ square centimetres. The volume of the solid, in cubic centimetres, is ?

• A. $192$
• B. $384$
• C. $480$
• D. $2592$

Answer 1

The correct option is A

$192$

Given that,

The surface areas of the six faces of a rectangular solid are $16,16,32,32,72$and $72$ square centimetres.

Let's consider areas of three faces, as opposite faces are equal in area :

• $l\times b=16$…………………(1)
• $b\times h=32$ ……………….(2)
• $l\times h=72$ …………………(3)

Multiply the equations (1), (2), (3), we will get

$(l\times b)\times (b\times h)\times (l\times h)=16\times 32\times 72$

${\left(l\right)}^2\times {\left(b\right)}^2\times {\left(h\right)}^2=\left(16\right)\times \left(32\right)\times \left(72\right)$

${\left(l\right)}^2\times {\left(b\right)}^2\times {\left(h\right)}^2=36864$

$(l\times b\times {h)}^2=36864$

$(l\times b\times h)=\sqrt{36864}$

$lbh=192$

Therefore, the volume of a solid is $192$ cubic centimetre.

Hence, the option is option A : $192$ $c{m}^3$.