Question

The edges of a cuboid are in the ratio 1:2:3 and its surface area is 88 cm${}^2$. The volume of the cuboid is:

• A. 24 cm³
• B. 48 cm³
• C. 64 cm³
• D. 12 m³
• E. 40 m³

Answer 1

The correct option is B

48 cm³

Let the dimensions of the cuboid be x, 2x and 3x.

Then, 2(x $\times$ 2x + 2x $\times$ 3x + x$\times$3x) =88

$\iff$ 2x${}^2$+6x${}^2$+3x${}^2$=44 $\iff$11x${}^2$=44$\iff$x${}^2$=4 $\iff$x=2

$\therefore$ Volume of the cuboid = (2 $\times$ 4 $\times$ 6) cm${}^3$ = 48 cm${}^3$