Question

The ratio of lateral surface area of a cone and that of hemisphere with equal height and equal radius is:
1. 2 ∶ 3
2. 1 ∶ 2
3. 2 ∶ √3
4. 1∶ √2

Answer 1

Correct Answer - Option 4 : 1∶ √2

Given:

radius = height

Concept:

Using the volume formula, calculate the ratio

Formula used:

Lateral surface area of hemisphere = 2πr2

Lateral surface area of cone = πrl

Lateral height (l) = √(r2 + h2)

Calculation:

Lateral height (l) = √(r2 + h2) = r√2

Lateral surface area of cone : Lateral surface area of hemisphere =  πr(r√2) : 2πr2

Lateral surface area of cone : Lateral surface area of hemisphere = 1 : √2