A 22.5 m high tent is in the shape of a frustum of a cone surmounted by a hemisphere. If the diameters of the upper and the lower circular ends of the frustum are 21 m and 39 m, respectively, then find the area of cloth (in m2) used to make the tent (ignoring the wastage). ( Use = 227 )

Answer: Option B

Solution

Answer: Option B

Solution:

$$\begin{array}{rl}& r=\frac{21}{2}\\ & R=\frac{39}{2}\\ & \text{Curved serface area of Hemisphere}\\ & =2\pi r^2\\ & =2\times \frac{22}{7}\times \frac{21\times 21}{2\times 2}\\ & =693\text{c}{\text{m}}^2\\ & H=\left(22.5-10.5\right)=12\text{ cm}\\ & L^2=H^2+{\left(R-r\right)}^2\\ & L^2=12^2+{\left(\frac{39}{2}-\frac{21}{2}\right)}^2\\ & L^2=144+81\\ & L=\sqrt{225}\\ & L=15\text{ cm}\\ & \text{Curved serface area of Frustum of cone}\\ & =\pi l\left(R+r\right)\\ & =\frac{22}{7}\times 15\times \left[\left(\frac{39}{2}\right)+\left(\frac{21}{2}\right)\right]\\ & =\frac{22}{7}\times 15\times 30\\ & =\frac{9900}{7}\text{ c}{\text{m}}^2\\ & =1414\frac{2}{7}\text{ c}{\text{m}}^2\\ & \therefore \text{Total area of cloth}\\ & =\left(693+1414\frac{2}{7}\right)\text{c}{\text{m}}^2\\ & =2107\frac{2}{7}\text{ c}{\text{m}}^2\end{array}$$