Question

Find the lateral surface area (in cm2) of a right circular cone which has base of perimeter 44 cm and height 24 cm?
1. 450 cm²
2. 550 cm²
3. 440 cm²
4. 500 cm²

Answer 1

Correct Answer - Option 2 : 550 cm²

Given:

The perimeter of the base of a right circular cone is 44 cm.

Height of the cone = 24 cm

Formula used:

The circumference of the base of the cone = 2πr

The curved surface area of the cone = πrl

The slant height of the cone (l) = √(h² + r²)

Where r → radius of the cone 

h → height of the cone 

l → slant height of the cone

Calculations:

According to the question,

The circumference of the base of the cone = 44 cm.

⇒ 2πr = 44

⇒ r = 7 cm

The slant height of the cone = √(h2 + r2)

⇒ l = √(242 + 72) = √(625) = 25

So, the curved surface area of the cone = πrl

⇒ (22/7) × 7 × 25 = 550 cm²

∴  The curved surface area of the cone is 550 cm2