Question

The length, breadth and height of a cuboid are in the ratio $5:4:2$. If the total surface area is $1216$ c$m^2$, find the dimensions of the solid.

• A. $(21\times 11\times 8)$ cm
• B. $(20\times 16\times 8)$ cm
• C. $(27\times 17\times 8)$ cm
• D. $(25\times 19\times 8)$ cm

Answer 1

The correct option is B $(20\times 16\times 8)$ cm

Given length,breadth height of a cuboid are in ratio $5:4:2$.

Total surface area of cuboid is $1216$ sq cm.
Let length, breadth and height of cuboid be $5x$, $4x$ and $2x$ respectively.
So, total surface area of cuboid $=2(lb+bh+lb)=2(5x\times 4x+4x\times 2x+5x\times 2x)=2(20x^2+8x^2+10x^2)=2\left(38x^2\right)=76x^2$
Total surface area of cuboid $=1216{cm}^2$
$\Rightarrow 76x^2=1216{cm}^2\Rightarrow x^2=16\Rightarrow x=4$
Dimensions of cuboid are :
Length $=5x=5\times 4=20$ m
Breadth $=4x=4\times 4=16$ m
Height $=2x=2\times 4=8$ m