Question

A box made of sheet metal costs ₹ 6480 at ₹ 120 per square metre. If the box is 5 m long and 3 m wide, find its height.

Answer 1

Length of the box =5 m
Breadth of the box =3 m

Area of the sheet required = $\frac{\mathrm{total}\mathrm{cost}}{\mathrm{cost}\mathrm{per}\mathrm{metre}\mathrm{square}}$

Let h m be the height of the box.
Then area of the sheet = total surface area of the box
$$\begin{gathered} =2(lb+lh+bh){\mathrm{m}}^2 \\ =2(5\times 3+5\times h+3\times h){\mathrm{m}}^2 \\ =2(15+8h)=(30+16h){\mathrm{m}}^2 \end{gathered}$$

$$\begin{gathered} \mathrm{Now},30+16h=\frac{6480}{120} \\ \Rightarrow 30+16h=54 \\ \Rightarrow 16h=24 \\ \Rightarrow h=1.5\mathrm{m} \end{gathered}$$

∴ The height of the box is 1.5 m.