The radius of the base of a cone is 9 cm and its height is 40 cm. What is its curved surface area? What is its total surface area?

(π = 3.14)

We have

Given: radius of the base of the cone, r = 9 cm

Height of the cone, h = 40 cm

First, we need to find slant height, l.

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

BC² = OB² + OC²

⇒ l² = r² + h²

⇒ l² = 9² + 40²

⇒ l² = 81 + 1600 = 1681

⇒ l = √1681

⇒ l = 41

Curved surface area of the cone is given by

CSA = πrl

Using r = 9 cm and l = 41 cm in above equation,

CSA = 3.14 × 9 × 41

⇒ CSA = 1158.66

Total surface area of the cone is given by

TSA = CSA + area of the base of the cone (area of solid circle)

⇒ TSA = 1158.66 + πr²

⇒ TSA = 1158.66 + (3.14 × 9²)

⇒ TSA = 1158.66 + 254.34

⇒ TSA = 1413

Thus, curved surface area is 1158.66 cm² and total surface area is 1413 cm².