Question

The dimensions of a box are in the ratio of 5: 2: 4 and its total surface area is 304 $m^2$. Find the volume of box.

• A. 540 m³
• B. 320 m³
• C. 180 m³
• D. 240 m³

Answer 1

The correct option is B

320 m³

Let the proportional constant be x

Length of box be 5x

Breadth of box be 2x

Height of box be 4x

By formula, surface area of cuboid = 2(lb + bh + lh)

2(5x.2x + 2x.4x + 5x.4x) = 304 $m^2$

(10 $x^2$ + 8 $x^2$ + 20 $x^2$) = 152 $m^2$

38 $x^2$ = 152 $m^2$

x = $\sqrt{4m^2}$

x = 2 m

Now, length of box = 5x = 5 $\times$ 2 = 10 m

Breadth of box = 2x = 2 $\times$ 2 = 4 m

Height of box = 4x = 4 $\times$ 2 = 8 m

So, volume of box = lbh

= 10 m $\times$ 4 m $\times$ 8 m

= 320 $m^3$