The height of a cone-shaped tent is 10 m and the radius of its base is 24 m.

(i) What is its slant height?

(ii) What is the amount of fabric required to make this tent? (π = 3.14)

We have

Given: height of the conic tent, h = 10 m

Radius of its base, r = 24 m

(i). In right-angled ∆BOC, using Pythagoras theorem

BC² = OB² + OC²

⇒ BC² = 24² + 10²

⇒ BC² = 576 + 100

⇒ BC² = 676

⇒ BC = √676 = 26

⇒ l = 26

(where l = slant height of the cone)

Thus, slant height of conic tent is 26 m.

(ii). To find the amount of fabric required to make the tent, we need to find curved surface area of the cone as the fabric is required to cover the curved surface not the base of the conic tent.

So, curved surface area of cone is given by

CSA = πrl

⇒ CSA = 3.14 × 24 × 26

⇒ CSA = 1959.36

Thus, 1959.36 m² of fabric is required to make this cone-shaped tent.