Question

If the area of the base of a cone is 38.5 cm² and the area of the curved surface is 231 cm². Find the slant height.
1. 21 cm
2. 41 cm
3. 16 cm
4. 18 cm

Answer 1

Correct Answer - Option 1 : 21 cm

Given

Area of base of a cone = 38.5 cm²

Curved surface area of cone = 231 cm²

Formula used 

Area of base = πr²

Area of curved surface area of cone = πrl

Where r and l are radius and slant height of cone respectively

(22/7) × r² = 38.5

⇒ r² = (38.5 × 7)/22

⇒ r = √12.25

⇒ r = 3.5 cm

⇒ πrl = 231

⇒ (22/7) × 3.5 × l = 231

⇒ l = (231 × 7)/(22 × 3.5)

⇒ l = 21 cm

∴ The slant height of a cone is 21 cm