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Question

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


Given: r:h=3:4 Let r=3x and h=4x

In the above figure, BC=r=3x and h=AB=4x

In ABC

AB2+BC2=AC2

16x2+9x2=AC2

AC=25x2=5x

Slant height of the cone is l=5x

Required ratio=total surface areacurved surface area=πr(r+l)πrl

=π×3x(3x+5x)π×3x×5x

=8:5


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