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 ?\[[Use \pi = \frac{22}{7}]\]

 

Answer 1

Given:
Diameter of the conical tent = 14 m
∴ Radius of the conical tent (r) = 7 m
Height of the conical tent (h) = 24 m

\[\text{Slant height of the conical tent} (l) = \sqrt{r^2 + h^2}\]
\[ = \sqrt{7^2 + {24}^2} m\]
\[ = \sqrt{625} m\]
\[ = 25 m\]

Curved surface area of the tent = \[\pi rl\]

\[= \left( \frac{22}{7} \times 7 \times 25 \right) m^2 \]
\[ = 550 m^2\]

Area of the cloth = Curved surface area of the tent
⇒ Length of the cloth ×">×× Width of the cloth = Curved surface area of the tent

⇒ Length of the cloth =\[\frac{\text{Curved surface area of the tent}}{\text{Width of the cloth}} = \frac{550}{5} m = 110 m\]

Cost of 1 metre of cloth = Rs 25
Cost of 110 m of cloth = Rs (25 ×">×× 110) =  Rs 2750