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
1. 4/9
2. 3/7
3. 5/9
4. 2/7
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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.