Question

The edges of a cuboid are in the ratio 1 : 2 : 3 and its surface area is $88c{m}^2$ The volume of the cuboid is :

• A. $120c{m}^3$
• B. $64c{m}^3$
• C. $48c{m}^3$
• D. $24c{m}^3$

Answer 1

The correct option is C $48c{m}^3$

Let the length of the cuboid $=x$, breadth $=2x$, 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 $=88{cm}^2$
$2(x\times 2x+2x\times 3x+x\times 3x)=88{cm}^2$
$22x^2=88$
$\therefore x=2$

Hence, the length of the cuboid $=x=2cm$, breadth $=2x=4cm$, height $=3x=6cm$

Volume of a cuboid $=l\times b\times h$

So, the volume of the cuboid with length $=2cm$, breadth $=4cm$ and height $=6cm=2\times 4\times 6=48{cm}^3$