Question

the radius of the base of a conical tent is 12 m and it's height is 9 m. find the area of canvas used to make the tent. also find the volume of air contained in the tent.

Answer 1

$$\begin{gathered} areaofcanvasused=lateralsurfaceareaofcone \\ =\mathrm{\pi rl} \\ \mathrm{Here}\mathrm{radius}=12\mathrm{m} \\ \mathrm{Height}=9\mathrm{m} \\ \mathrm{So}\mathrm{lateral}\mathrm{height}=\sqrt{{\mathrm{r}}^2+{\mathrm{h}}^2}=\sqrt{81+144}=15 \\ \mathrm{So}\mathrm{a}\mathrm{r}\mathrm{e}\mathrm{a}\mathrm{o}\mathrm{f}\mathrm{c}\mathrm{a}\mathrm{n}\mathrm{v}\mathrm{a}\mathrm{s}\mathrm{u}\mathrm{s}\mathrm{e}\mathrm{d}=\frac{22}{7}\times 12\times 15=565.71{\mathrm{m}}^2 \\ \mathrm{volume}\mathrm{of}\mathrm{air}\mathrm{contained}={\mathrm{\pi r}}^2\mathrm{h}=\frac{22}{7}\times {12}^2\times 9 \\ =4073.14{\mathrm{m}}^3 \end{gathered}$$