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

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Answer

Given, ratio of slant height = 5 : 4

Let slant height of 1st cone be 5x cm and 2nd cone be 4x cm.

For 1st cone,

⇒ Diameter = d1

⇒ Radius = r1

⇒ Slant height (l1) = 5x

For 2nd cone,

⇒ Diameter = d2

⇒ Radius = r2

⇒ Slant height (l2) = 4x

Given,

⇒ d1 = d2

∴ r1 = r2.

CSA of 1st coneCSA of 2nd cone=πr1l1πr2l2=l1l2=5x4x=54=5:4.\Rightarrow \dfrac{\text{CSA of 1st cone}}{\text{CSA of 2nd cone}} = \dfrac{πr1l1}{πr2l2} \\[1em] = \dfrac{l1}{l2} = \dfrac{5x}{4x} \\[1em] = \dfrac{5}{4} = 5 : 4.

Hence, ratio of curved surface areas = 5 : 4.

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