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Mathematics

The radii of two solid cones are equal and their slant heights are in the ratio 7 : 4. The ratio between their curved surface areas is :

  1. 4 : 7

  2. 7 : 4

  3. 16 : 49

  4. 49 : 16

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Answer

Let radii of both the cones be r units each.

Let slant height of two cones be l1 and l2.

Curved surface area of first cone = πrl1

Curved surface area of second cone = πrl2

CSA of 1st coneCSA of 2nd cone=πrl1πrl2=l1l2=74\dfrac{\text{CSA of 1st cone}}{\text{CSA of 2nd cone}} = \dfrac{πrl1}{πrl2} = \dfrac{l1}{l2} = \dfrac{7}{4} = 7 : 4.

Hence, Option 2 is the correct option.

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