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in Surface Areas And Volumes by (15 points)
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The diameters of two cones are equal if their slant height are in the ratio 7:4 find the ratio of their curved surface area.

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Curved surface area = π × r × l

Since the two cones have the same diameter, the radius should be the same (r).

As for the slanted height, since the ratio 7:4 is given, we can assume the slanted height is 7x and 4x. So, we can find the ratio of their curved surface area by eliminate the same factor (π r x) for the two terms (as shown below)

Ratio

= π r (7x) : π r (4x) 

= 7:4

Therefore, the ratio between the curved surface area is also equal to 7:4.

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