Question

The surface areas of six faces of a cuboid are 12, 12, 36, 36, 48, 48, (all in $c{m}^2)$. The volume of the solid in $c{m}^3$, is

• A. 144 cm³
• B. 169 cm³
• C. 64 cm³
• D. 216 cm³

Answer 1

The correct option is A

144 cm³

Let the dimension of a cuboid be l, b, and h.

Since the six surface areas are given:

$\Rightarrow$ l $\times$ b = 12.......................................(1)

$\Rightarrow$ b $\times$ h = 36.......................................(2)

$\Rightarrow$ l $\times$ h = 48.......................................(3)

Now multiplying equation (1),(2) and (3), we get

$\Rightarrow$ (l $\times$ b) $\times$ (b $\times$ h) $\times$ (l $\times$ h) = 12 $\times$ 36 $\times$ 48

$\Rightarrow$ $(l\times b\times h{)}^2$ = 20736

$\Rightarrow (l\times b\times h)=\sqrt{20736}=144c{m}^3$

Since volume of a cuboid is given by:

$\text{V}=(l\times b\times h)=144c{m}^3$

So the correct answer is Option A.