Question

The length breadth and height of a cuboid are in the ratio 5 : 4 : 2 and the total surface area is $1216c{m}^2$, then the volume of the cuboid is

• A. 2460 $c{m}^3$
• B. 2560 $c{m}^3$
• C. 2660 $c{m}^3$
• D. 2700 $c{m}^3$

Answer 1

The correct option is B 2560 $c{m}^3$

Given length , breadth and height of cuboid are in ratio 5:4:3

Let length , breadth and height of cuboid are 5a,4a and 2a respt

Then surface area of cuboid =$2(5a\times 4a+4a\times 2a+5a\times 2a)=2(20a^2+8^2+10a^2)=76a^2$ sq cm

But surface area is given 1216 sq cm

$\therefore 76a^2=1216\Rightarrow a^2=16\Rightarrow a=4$

Then the sides of cuboid is 20 cm ,16 cm and 8 cm

Then volume of cuboid =$20\times 16\times 8=2560c{m}^3$