Question

The length, width and height of rectangular solid are in the ratio of 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. $32c{m}^2$
• C. $44c{m}^2$
• D. $88c{m}^2$

Answer 1

The correct option is D

$88c{m}^2$

$\text{Ratio of dimensions of the cuboid}=3:2:1$

$\text{Let length}=3x$

$\text{Breadth}=2x$

$\text{Height}=x$

$\text{Then, volume}=lbh=3x\times 2x\times x=6x^3$

$\therefore 6x^3=48\Rightarrow x^3=\frac{48}{6}=8=(2{)}^3$

$\therefore x=2cm$

$\therefore \text{Length (l)}=3\times 2=6cm$

$\text{Breadth (b)}=2\times 2=4cm$

$\text{Height (h)}=1\times 2=2cm$

$\text{Now surface area}=2[lb+bh+hl]$

$=2[6\times 4+4\times 2+2\times 6]c{m}^2$

$=2[24+8+12]=2\times 44c{m}^2$

$=88c{m}^2$