Question

The length of a cuboid is twice its breadth. The breadth is twice its height. Find the ratio of the lateral surface area to the total surface area of the cuboid. Given that the height of the cuboid is $4\text{cm}$.

• A.
  $7:6$
• B.
  $2:7$
• C.
  $7:2$
• D.
  $3:7$

Answer 1

The correct option is D

$3:7$
Given, the height of cuboid is $4\text{cm}$.
Also, it given that the length of a cuboid is twice its breadth and the breadth is twice its height.
$\therefore \text{breadth}=2\times \text{height}$
$=2\times 4=8\text{cm}$
$\text{length}=2\times \text{breadth}$
$=2\times 8=16\text{cm}$
So,
Length, $l=16cm$
Breadth, $b=8cm$
Height, $h=4cm$

Lateral surface area $=2(lh+bh)$
$=2(16\times 4+8\times 4)$
$=192c{m}^2$
Total surface area $=2(lb+bh+hl)$
$=2(16\times 8+8\times 4+4\times 16)$
$=448c{m}^2$

Ratio $=\frac{\text{lateral surface area}}{\text{total surface area}}$

$=\frac{192}{448}$
$=3:7$