Correct Answer - Option 1 : 21 cm

**Given**

Area of base of a cone = 38.5 cm^{2}

Curved surface area of cone = 231 cm^{2}

**Formula used **

Area of base = πr^{2}

Area of curved surface area of cone = πrl

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

(22/7) × r^{2} = 38.5

⇒ r^{2} = (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**