Question

Find the area of the sheet required to make a cylindrical container which is open at one side and whose diameter is 28 cm and height is 20 cm. Find the approximate area of the sheet required to make a lid of height 2 cm for this container.

Answer 1

Diameter = 28 cm
Radius = 14 cm
Height = 20 cm
Curved surface area of the cylinder + area of the base = area of the sheet
$$\begin{gathered} \Rightarrow \mathrm{Area}\mathrm{of}\mathrm{sheet}=2\mathrm{\pi }rh+\mathrm{\pi }{r}^2 \\ \Rightarrow \mathrm{Area}\mathrm{of}\mathrm{sheet}=\mathrm{\pi }r\left(2h+r\right) \\ \Rightarrow \mathrm{Area}\mathrm{of}\mathrm{sheet}=\frac{22}{7}\times 14\left(2\times 20+14\right) \\ \Rightarrow \mathrm{Area}\mathrm{of}\mathrm{sheet}=2376 \end{gathered}$$
Thus, area of sheet required = 2376 cm²
Area of sheet required to make a lid of height 2 cm will be
$$\begin{gathered} \mathrm{Area}\mathrm{of}\mathrm{sheet}=2\mathrm{\pi }rh+\mathrm{\pi }{r}^2 \\ =\mathrm{\pi }r\left(2h+r\right) \\ =\frac{22}{7}\times 14\left(2\times 2+14\right) \\ =44\times 18 \\ =792 \end{gathered}$$
Thus, area of sheet used to make the lid is 792 sq cm.