Question

A brick has length (l), breadth (b) and height (h) in the ratio 1:2:3, the total surface area of the brick is 792 sq. m. Find its volume.

• A. 1296 $m^3$
• B. 1396 $m^3$
• C. 1496 $m^3$
• D. 1596 $m^3$

Answer 1

The correct option is A

1296 $m^3$

Given - I:b:h = 1:2:3

Let the length be x. Then b = 2x, h = 3x

As per question:

2(lb + bh + hl) = 792

2(2$x^2$+6$x^2$+3$x^2)$ = 792

$\Rightarrow$ 11 $x^2$ = $\frac{792}{2}$

$\Rightarrow$ $x^2$ = $\frac{396}{11}$ = 36

$\Rightarrow$ x = 6 m

l = 6m, b = 2 $\times$ 6 = 12m and h = 3 $\times$ 6 = 18m

Hence volume= lbh= 6$\times$12$\times$18 = 1296 $m^3$