Question

The volume of a cone is 154 cm³ and its height is 12 cm. Find the lateral surface area of the cone?

1. 157.5 cm²
2. 142.5 cm²
3. 137.5 cm²
4. 150.5 cm²

Answer 1

Correct Answer - Option 3 : 137.5 cm²

Given:

Volume of cone = 154 cm³

Height of cone = 12 cm

Concept:

Using the volume formula, calculate the radius of the cone and then calculate the lateral height.

Formula used:

Volume of cone = (1/3)πr²h

Lateral surface area of cone = πrl

Lateral height (l) = √(r² + h²)

Calculation:

∵ Volume of cone = (1/3)πr²h

⇒ 154 = (1 × 22 × r² × 12)/(3 × 7)

⇒ 154 × 3 × 7 = 22 × r² × 12

⇒ r² = (154 × 3 × 7)/( 22 × 12)

⇒ r² = 49/4

⇒ r = √(49/4) = 7/2

∵ Lateral height (l) = √(r² + h²)

⇒ l = √[(7/2)² + (12)²]

⇒ l = √[144 + (49/4)]

⇒ l = √[(576 + 49)/4]

⇒ l = √(625/4)

⇒ l = 25/2 cm

∴ Lateral surface area of cone = πrl

= (22/7) × (7/2) × (25/2)

= 275/2 cm²

= 137.5 cm²