Question

The length, width and height of a rectangular solids are in ratio $3:2:1$.
If the volume of the box is $48c{m}^3$, the total surface area of the box is:

• A. $27c{m}^2$
• B. $88c{m}^2$
• C. $44c{m}^2$
• D. $32c{m}^2$

Answer 1

The correct option is B $88c{m}^2$

Given: Ratio of length, width and height of a rectangular solid $=3:2:1$

Let $l=3x,b=2x$ and $h=x$

As, volume of box $=48c{m}^3$

$l\times b\times h=48$

$3x\times 2x\times x=48$

$6x^3=48$

$x^3=8$

$x=2cm$

$\therefore$ Total surface area $=2(lb+bh+lh)$

$=2(3x\times 2x+2x\times x+3x\times x)$

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

$=2\left(11x^2\right)$

$=22x^2$

$=22\left(4\right)$

$=88c{m}^2$

Hence, (d) is the correct option.