Question

A conical tent is 10 m high and its base radius is 24 m.
Find (i) the slant height of the tent and (ii) the cost of canvas required to make the tent, if the cost of 1 m² of canvas is Rs 70.

Answer 1

(i)
$$\begin{gathered} l^2=\sqrt{r^2+h^2} \\ =\sqrt{{24}^2+{10}^2} \\ =\sqrt{576+100} \\ =\sqrt{676} \\ =26\mathrm{m} \end{gathered}$$
So, slant height of the cone = 26 m

(ii) Curved surface area of the cone = $\mathrm{\pi }rl$

= $\frac{22}{7}\times 24\times 26{\mathrm{m}}^2$
Cost of 1 m² area of the canvas = Rs 70
Cost of $\frac{22}{7}\times 24\times 26{\mathrm{m}}^2$ = $\frac{22}{7}\times 24\times 26\times 70=\mathrm{Rs}137280$