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Question

The diameters of two cones are equal. If their slant heights are in the ratio 5:4, then the ratio of their curved surface areas is ________.

A
4:5
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B
25:16
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C
16:25
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D
5:4
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Solution

The correct option is D 5:4
Given, diameters of two cones are equal.
We know that, diameter = radius2
Implies radii of the two cones are also equal
Given, the slant heights are in the ratio 5:4.
Let the slant height of 1st cone be l1 and slant height of 2nd cone be l2.

Curved surface area of the first cone =πrl1
Curved surface area of the second cone
=πrl2

Now, ratio of their curved surface areas
=πrl1πrl2=l1l2=54

So, the ratio of curved surface areas is 5:4.

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