Question

The height and radius of cone are 4 cm and 3 cm respectively. Fnd the curved surface area of cone.

• A. $14\pi {cm}^2$
• B. $16\pi {cm}^2$
• C. $15\pi {cm}^2$
• D. $12\pi {cm}^2$

Answer 1

The correct option is C

$15\pi {cm}^2$

Given, height of the cone, h = 4 cm
radius of the cone, r = 3 cm

As we revolve a right-angled triangle about its height, we will get a cone. Therefore, slant height is the hypotenuse of the corresponding right-angled triangle.
By using Pythagoras' theorem, we get,
Slant height, $l=\sqrt{h^2+r^2}=\sqrt{4^2+3^2}=5cm$

Surface area of the cone = $\pi rl$
= $\pi$ $\times$3 $\times$ 5
= 15$\pi$ ${cm}^2$