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.