Question

The ratio between the radius and height of a cone is 4 : 3. Find the ratio between lateral surface area and total surface area of the cone?
1. 4/9
2. 3/7
3. 5/9
4. 2/7

Answer 1

Correct Answer - Option 3 : 5/9

Given:

The ratio of radius and height = 4 : 3

Formula used:

The lateral surface area of cone = πrl

The total surface area of cone = πr(l + r)

l² = r² + h²

Where,

r = radius of cone

l = slant height of the cone

Calculation:

Let r = 4 and h = 3

l² = r² + h²

⇒ l² = 4² + 3²

⇒ l = 5

The ratio between lateral surface area and total surface area of the cone

⇒ (πrl)/[ πr(l + r)]

⇒ l/(l + r)

⇒ 5/(5 + 4)

⇒ 5/9

∴ The ratio between lateral surface area and total surface area of the cone is 5/9.