Question

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

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

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

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

Since volume of a cuboid is calculated as ${}^{\prime }l\times b\times h^{\prime }$, the required volume is $144c{m}^3$.