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KVPY2011MathematicsApplication of Derivatives

The diameter of one of the bases of a truncated cone is 100 ~mm . If the diameter of this base is increased by 21 % such that it still remains a truncated cone with the height and the other base unchanged, the volume also increases by 21 % . The radius of the other base (in mm ) is-

Options

  1. A65
  2. B55
  3. C45
  4. D35

Correct answer

B. 55

Step-by-step solution

Let initially 2 bases have radii 5 ~cm and r cm . Finally base have radii (1.21 5) and r . Ratios of volumes = V₂ V₁ =1.21 array l V ₂= h 3 [(6.05)²+(6.05) r + r ² ] V ₁= h 3 [5²+5 r + r ² ] V ₂ ~V ₁ =1.21 (6.05)²+(6.05) r + r ² 5²+5 r + r ² =1.21 r ²= 6.3525 21 r = 11 2 ~cm =55 ~mm array

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