Question

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?

Answer 1

Radius of the cone (r) =7 cm
Height of the cone (h) =24 cm
The height and radius of a cone form a right angle.
Suppose the slant height is l cm.
By Pythagoras Theorem,
l² = r² + h²
⇒ l² = 7² + 24²
⇒ l² = 49 + 576
⇒ l² = 625
⇒ l = 25 cm
The amount of paper required to make 1 conical cap = Curved surface area of a cone
= πrl
$$\begin{gathered} =\frac{22}{7}\times 7\times 25 \\ =550\mathrm{Sq}\mathrm{cm} \end{gathered}$$

The amount of paper required to make 10 conical caps = Curved surface area of a cone × 10
= 550 × 10 sq cm
= 5500 sq cm