Question

The length breadth and height of a cuboid are in ratio 6 : 5 : 3. If its total surface area is 504 $c{m}^2$, then find its dimensions.

• A. 12 cm, 10 cm and 6 cm
• B. 22 cm, 10 cm and 6 cm
• C. 24 cm, 20 cm and 12 cm
• D. 16 cm, 10 cm and 6 cm

Answer 1

The correct option is A 12 cm, 10 cm and 6 cm

Given
Total surface area of cuboid = 504 $c{m}^2$
Let the length, breadth and height of the cuboid be 6$x$, 5$x$ and 3$x$ respectively.
We know that
$\because$ Total surface area of cuboid
= 2 (lb + bh + hl)
$\Rightarrow 2(6x\times 5x+5x\times 3x+3x\times 6x)$ = 504 $c{m}^2$
$\Rightarrow 126x^2=504c{m}^2$
$\Rightarrow x^2=\frac{504}{126}c{m}^2$
$\Rightarrow x=2cm$
$\therefore$ length = 6$x$ = 12cm
breadth = 5$x$ = 10 cm
height = 3$x$ = 6cm