Question

The perimeter of the base of a cone height 11 cm, is 44 cm .find the total surface area of a cone.

Answer 1

Given:

• Perimeter of base of cone = 44 cm
• Height of cone = 11 cm

To find:

• Total Surface area of cone = ?

Solution:

Base of cone is a circle.

Perimeter of circle = 2πr

⇒ 44 = (2 × 22 × r) ÷ 7

⇒ 44 = 44r ÷ 7

⇒ 44 × 7 = 44r

⇒ r = 7 cm

By Pythagoras theorem,

l² = r² + h²

⇒ l² = 7² + 11²

⇒ l² = 170

⇒ l = √170

⇒ l = 13.03 cm

Total Surface area of cone = πr (r + l)

⇒ TSA of cone = 7π (20.03)

⇒ TSA of cone = 7 × 22/7 (20.03)

⇒ TSA of cone = 22 (20.03)

⇒ TSA of cone = 440.66 cm²

∴ TSA of cone = 440.66 cm²