Question

A 5 m wide cloth is used to make a conical tent of base diameter 14 m and height 24 m. Find the cost of cloth used at the rate of Rs 25 per metre. [Use π = 22/7] [CBSE 2014]

Answer 1

Let the slant height of the cone be l.
Thus , the slant height is given by
$$\begin{gathered} l=\sqrt{{\left(\frac{14}{2}\right)}^2+{\left(24\right)}^2} \\ =\sqrt{49+576} \\ =\sqrt{625} \\ =25\mathrm{m} \end{gathered}$$
Now, the curved surface area of the tent is given by
$$\begin{gathered} \frac{22}{7}\times \frac{14}{2}\times 25 \\ =550{\mathrm{m}}^2 \end{gathered}$$
The curved surface area will be equal to the area of the cloth
$$\begin{gathered} \Rightarrow 550=\mathrm{Length}\times 5 \\ \Rightarrow \mathrm{Length}=110\mathrm{m} \end{gathered}$$
Now, the cost of cloth is given by
110 ⨯ 25
= Rs 2750