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Question

The radius and height of a right circular cone are in the ratio 3:4. Then the ratio of total surface area of the cone to its curved surface area is


A

2:3

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B

3:5

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C

7:9

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D

8:5

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Solution

The correct option is D

8:5


Let 'r' be the radius of the cone and 'h' be its height.
Given, r : h = 3 : 4.
Let r=3x and h=4x.
We know, slant height is given by,
l=h2+r2
l=(3x)2+(4x)2
l=5x

Required ratio =TSACSA=πr(r+l)πrl=(r+l)l=(3x+5x)5x=8x5x

Required ratio=8:5


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