Question

The length of a cuboid is twice its breadth. The breadth is twice its height. Then ratio of LSA to TSA of cuboid will be ___.

• A. $7:2$
• B. $7:3$
• C. $3:7$
• D. $7:4$

Answer 1

The correct option is C $3:7$

Let the height of the cuboid be '$h$' units.
Breadth of cuboid ($b$) = 2$h$
Length of cuboid ($l$) = 2b = 4$h$

Lateral surface area = $2(lh+bh)$
$=2(4h\times h+2h\times h)$
$=12h^2$
Total surface area $=2(lb+bh+lh)=2(4h\times 2h+2h\times h+4h\times h)=28h^2$
$\frac{\text{Lateral Surface Area}}{\text{Total Surface Area}}=\frac{12h^2}{28h^2}=3:7$