Question

A conical tent is $10m$ high and the radius of its base is$24m$. Find slant height of the tent and cost of the canvas required to make the tent, if the cost of $1m^2$ canvas is $Rs.70$.

Answer 1

Step 1 - Finding the slant height of the tent.

It is given that, radius of conical tent $=24m$ and height of the conical tent $=10m$

Now, by the relation between the slant height, radius and height of the cone

$$\begin{gathered} l^2=r^2+h^2 \\ {l}^2={24}^2+{10}^2 \\ {l}^2=576+100 \\ {l}^2=676 \\ l=\sqrt{676} \\ l=26m \end{gathered}$$

Therefore the slant height of the cone is $26m$.

Step 2 - Finding the cost of the canvas

To Find the cost of the canvas we need to find the curved surface area of the Cone.

Curved surface area of the cone $=\pi rl$

$$\begin{gathered} =\frac{22}{7}\times 24\times 26 \\ =\frac{13728}{7}{\mathrm{m}}^2 \end{gathered}$$

Cost of $1m^2$ canvas = $₹70$

Therefore, the cost of $\frac{13728}{7}{m}^2$ canvas = $\frac{13728}{7}\times 70=137280$

Hence, the cost of canvas of the conical tent $₹137280$.