Question

The length, the breadth and the height of a cuboid are in the ratio 5: 3: 2. If its volume is $240c{m}^3$, then find the total surface area of the cuboid in $c{m}^2$.

Answer 1

Let the length of the cuboid $=5x$, breadth $=3x$, height $=2x$
Volume of a cuboid of length l, breadth b and height h $=l\times b\times h$

Given, volume of the cuboid $=240{cm}^3$

$=>5x\times 3x\times 2x=240{cm}^3$
$=>x^3=8$

$=>x=2$

Hence, the length of the cuboid $=5x=10cm$, breadth $=3x=6cm$, height $=2x=4cm$

Total surface area of a cuboid of length l, breadth b and height h $=2(l\times b+b\times h+l\times h)$
So, the total surface area of the cuboid with length $=10cm$, breadth $=6cm$ and height $=4cm=2(10\times 6+6\times 4+4\times 10)=2(60+24+40)=248{cm}^2$