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.