The height of a cone-shaped paper hat is 24 cm and the radius of the base is 7 cm. How much paper will be required to make 10 such hats?

We have

Given: height of the cone, h = 24 cm

Radius of the base of the cone, r = 7 cm

In right-angled ∆BOC, using Pythagoras theorem, we can write

BC² = OB² + OC²

⇒ BC² = 7² + 24²

⇒ BC² = 49 + 576 = 625

⇒ BC = √625 = 25

⇒ l = 25 cm

⇒ slant height of the cone = 25 cm

If this is a hat (cone-shaped), then the paper will cover only the curved surface of the hat, not the base. Base of the hat remains open.

So, we just need to find curved surface area of the cone, which is given by

CSA = πrl

Substituting values r = 7 cm and l = 25 cm in the above equation, we get

CSA = 22/7 × 7 × 25

⇒ CSA = (22 × 7 × 25)/7

⇒ CSA = 550

The paper required to make 1 hat = 550 cm²

Then, paper required to make 10 hats = 550 × 10 = 5500 cm²

Thus, paper required to make 10 hats is 5500 cm².