Question

The length of a cuboid is twice its breadth. The breadth is twice its height. Then, the ratio of LSA to TSA is .

• A. $7:3$
• B. $3:7$
• C. $7:2$

Answer 1

The correct option is B $3:7$

Let, $l$ be the length, $b$ be the breadth and $h$ be the height.

Given, length of the cuboid $\left(l\right)=2b$,
breadth of the cuboid $\left(b\right)=2h$,
Therefore, $l=2\times 2h=4h$,
where h is the height of the cuboid.

Lateral surface area
$=2(lh+bh)=2(4h\times h+2h\times h)=12h^2$

Total surface area
$=2(lb+bh+lh)=2(4h\times 2h+2h\times h+4h\times h)=28h^2$

$\text{Ratio}$
$=\frac{\text{Lateral surface area}}{\text{Total surface area}}=\frac{12h^2}{28h^2}=\frac{3}{7}$

Therefore, the ratio of LSA to TSA is $3:7.$