3 Tutor System
Starting just at 265/hour

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

i) Let ABC be a conical tent.
Given :
Height (h) of conical tent = 10 m
Radius (r) of conical tent = 24 m

Let the slant height of the tent be l.
In $$\triangle{ABO}$$,
$$\Rightarrow$$ $${AB}^2 = {AO}^2 + {BO}^2$$
$$\Rightarrow$$ $${l}^2 = {h}^2 + {r}^2$$
$$\Rightarrow$$ $$l^2= {10}^2 + {24}^2 {m}^2$$
$$\Rightarrow$$ $$l^2= 676 {m}^2$$
$$\Rightarrow$$ $${l}^2 = {26}^2 m$$
$$\Rightarrow$$ l = 26 m

Therefore, the slant height Of the tent is 26 m.

ii) We know, CSA of tent
= $${\pi}rl$$
= [$$\frac{22}{7} × 24 × 26 m$$]
= $$\frac{13728}{7} {m}^2$$

Cost of 1 $${m}^2$$ canvas = Rs. 70
Cost of [$$\frac{13728}{7} {m}^2$$] canvas
= Rs. [$$\frac{13728}{7} × 70$$ $${m}^2$$]
= Rs. 137280.

Therefore, the cost of the canvas required to make such a tent is Rs. 137280.