Question

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

• A. 420
• B. 720
• C. 680
• D. 460

Answer 1

The correct option is B 720

Let the length of the cuboid $=6x$, breadth $=5x$, height $=3x$
Total surface area of a cuboid of length l, breadth b and height h
$=2(l\times b+b\times h+l\times h)$
Given, total surface area of the cuboid $=504{cm}^2$
$2(6x\times 5x+5x\times 3x+6x\times 3x)=504{cm}^2$
$126x^2=504$
$=>x=2$

Hence, the length of the cuboid $=6x=12cm$, breadth $=5x=10cm$, height $=3x=6cm$

Volumeof a cuboid of length l, breadth b and height h $=l\times b\times h$
So, the volume of the cuboid with length $=12cm$, breadth $=10cm$ and height $=6cm=12\times 10\times 6=720{cm}^3$