Question

A cubical box has each edge 10 cm and another cuboidal box is 12.5 cm long.10 wide and 8 cm high.
(i) Which box has the greater lateral surface area and by how much?
(ii) Which box has the smaller total surface area and by how much?

Answer 1

(i) Lateral surface area of cube = $4edg{e}^2$

$\begin{array}{c}=4{\left(10\right)}^2\\ =400\end{array}$

lateral surface area of cuboid =$2h\left(l+b\right)$

$\begin{array}{c}2\times 8\left(12.5+10\right)\\ =16\times 22.5\\ =360\end{array}$

So, the lateral surface area of the cube is larger by $(400-360=40)$$c{m}^2$

(ii) Total surface area of cube = $6edg{e}^2$

$\begin{array}{c}=6{\left(10\right)}^2\\ =600\end{array}$

lateral surface area of cuboid =$2\left(lb+bh+hl\right)$

$\begin{array}{c}2\left(12.5\times 10+10\times 8+8\times 12.5\right)\\ =2\left(125+80+100\right)\\ =610\end{array}$

So, the total surface area of cuboid is larger by $(610-600=10)$ $c{m}^2$