Question

The surface areas of six faces of a cuboid are 12, 12, 36, 3648, 48, (all in cm²). Find the volume of the solid in cm³.

• 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 the cuboid be lbh.

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

$\Rightarrow$ (lb)(bh)(lh) = 12 $\times$ 36 $\times$ 48

$\Rightarrow$ $(lbh{)}^2$ = 20736

$\Rightarrow$ (lbh) = $\sqrt{20736}$ = 144 $c{m}^3$

Since volume of a cuboid is given by:

V = (lbh) = 144 $c{m}^3$

So the correct answer is Option A.