Question

A tent is in the shape of a right circular cylinder up to a height of 3 m and conical above it. The total height of the tent is 13.5 m and the radius of its base is 14 m. Find the cost of cloth required to make the tent at the rate of Rs 80 per square metre.

Answer 1

Radius of the cylinder = 14 m
Radius of the base of the cone = 14 m
Height of the cylinder (h) = 3 m
Total height of the tent = 13.5 m
Surface area of the cylinder$=2\pi rh=\left(2\times \frac{22}{7}\times 14\times 3\right){\mathrm{m}}^2=264{\mathrm{m}}^2$

Height of the cone$=\mathrm{Total}\mathrm{height}-\mathrm{Height}\mathrm{of}\mathrm{cone}=\left(13.5-3\right)\mathrm{m}=10.5\mathrm{m}$

Surface area of the cone = $\pi r\sqrt{r^2+h^2}$

$$\begin{gathered} =\pi r\sqrt{r^2+h^2}=\left(\frac{22}{7}\times 14\times \sqrt{{14}^2+10.5^2}\right){\mathrm{m}}^2 \\ =\left(44\times \sqrt{196+110.25}\right){\mathrm{m}}^2=\left(44\times \sqrt{306.25}\right){\mathrm{m}}^2 \\ =\left(44\times 17.5\right){\mathrm{m}}^2=770{\mathrm{m}}^2 \end{gathered}$$

Total surface area $=(264+770){\mathrm{m}}^2=1034{\mathrm{m}}^2$

∴ Cost of cloth$=\mathrm{Rs}1034\times 80=\mathrm{Rs}82720$