Question

The lateral surface area of a cuboid is $224{cm}^2$. Its height is $7cm$ and the base is a square. Find
(i) side of the square base
(ii) the volume of the cuboid

Answer 1

Given

Lateral surface area of a cuboid is $224{cm}^2$

Height $\left(h\right)=7cm$

(i) $2(l+b)\times h=224$

$\Rightarrow$ $2(l+b)\times 7=224$

$\Rightarrow l+b=\frac{224}{14}=16cm$

But $l=b$(Since the base of cuboid is a square)

So, $2\times side=16cm$

$\Rightarrow$ side $=\frac{16}{2}=8cm$

(ii) Volume of cuboid $=lbh=8\times 8\times 7{cm}^3=448{cm}^3$