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Cylinder to Cones Volume

CMAT 2024 · Quantitative Techniques & Data Interpretation · Medium · Geometry

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Ice-cream, completely filled in a cylinder of diameter 35 cm and height 32 cm, is to be served by completely filling identical disposable cones of diameter 4 cm and height 7 cm. The maximum number of cones that can be used in this way is

  1. A.

    950

  2. B.

    1000

  3. C.

    1050

  4. D.

    1100

Answer

C

Explanation

Volume of cylinder =πR2H=π(17.5)2×32= \pi R^2 H = \pi (17.5)^2 \times 32. Volume of one cone =13πr2h=13π(2)2×7= \frac{1}{3} \pi r^2 h = \frac{1}{3} \pi (2)^2 \times 7.

Number of cones=π(17.5)2×3213π×4×7=306.25×32×328=1050\text{Number of cones} = \frac{\pi (17.5)^2 \times 32}{\frac{1}{3} \pi \times 4 \times 7} = \frac{306.25 \times 32 \times 3}{28} = 1050

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