Question

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 m2 canvas is 70.

Answer 1

(i) Let ABC be a conical tent.
Height (h) of conical tent = 10 m
Radius (r) of conical tent = 24 m
Let the slant height of the tent be l.
In $∆$ABO, AB2 = AO2 + BO2
l2 = h2 + r2
= (10 m)2 + (24 m)2
I= $\sqrt{676}$
= 26 m
Therefore, the slant height of the tent is 26 m.

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(ii) curved surface area of the cone = $\pi rl$
= $\frac{22}{7}$ × 24 m × 26 m
= $\frac{13728}{7}$m²

The cost of the canvas required to make the tent, at $₹$ 70 per m² = 70 × Curved surface area of the cone
= $\frac{13728}{7}$ × 70
= $₹$137280

Thus, slant height of the tent is 26 m and the cost of the canvas is ₹ 137280.