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 5:4Given, 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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