The volume of a conical tent is 1232 m3 and the area of its base is 154 sq. m. Find the length of the canvas required to build the tent, if the canvas is 2 m in width. ( Take = 227 )

Answer: Option D

Solution

Answer: Option D

Solution:

$$\begin{array}{rl}& \pi r^2=154\\ & r^2=\frac{154\times 7}{22}\\ & r^2=49\\ & r=\sqrt{49}\\ & r=7\text{ m}\\ & \text{Also volume}=1232\\ & \frac{1}{3}\pi r^{2}h=1232\\ & h=\frac{1232\times 3}{\pi r^2}\\ & h=\frac{1232\times 3}{154}\\ & h=24\text{ m}\\ & \text{Area of canvas required}=\pi rl\\ & =\pi r\sqrt{r^2+h^2}\\ & =\frac{22}{7}\times 7\times \sqrt{{24}^2+7^2}\\ & =\frac{22}{7}\times 7\times 25\\ & =550{\text{m}}^2\\ & \text{Length}\times \text{2}=550{\text{m}}^2\\ & \text{length}\left(l\right)=\frac{550}{2}=275\text{ m}\end{array}$$