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Change in volume of cone

CMAT 2018 · Quantitative Techniques & Data Interpretation · Easy · Mensuration

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If the height of a right circular cone is increased by 200% and the radius of the base is reduced by 50%, then the volume of the cone:

  1. A.

    Remains unaltered

  2. B.

    Decreases by 25%

  3. C.

    Increases by 25%

  4. D.

    Increases by 50%

Answer

B

Explanation

Initial Volume V=13πr2hV = \frac{1}{3} \pi r^2 h.

New height h′=h+2h=3hh' = h + 2h = 3h. New radius r′=0.5rr' = 0.5r.

New Volume V′=13π(0.5r)2(3h)=13π(0.25r2)(3h)=0.75VV' = \frac{1}{3} \pi (0.5r)^2 (3h) = \frac{1}{3} \pi (0.25 r^2) (3h) = 0.75 V.

Change in volume = 0.75V−V=−0.25V0.75V - V = -0.25V, which is a decrease of 25%.

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