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Mensuration: Cylinder to Cones

XAT 2019 · Quantitative Ability & Data Interpretation · Easy · Geometry

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A gold ingot in the shape of a cylinder is melted and the resulting molten metal molded into a few identical conical ingots. If the height of each cone is half the height of the original cylinder and the area of the circular base of each cone is one fifth that of the circular base of the cylinder, then how many conical ingots can be made?

  1. A.

    60

  2. B.

    10

  3. C.

    30

  4. D.

    20

  5. E.

    40

Answer

C

Explanation

Volume of cylinder Vcyl=A⋅HV_{cyl} = A \cdot H. Volume of cone Vcone=13Acone⋅hcone=13(A5)(H2)=A⋅H30V_{cone} = \frac{1}{3} A_{cone} \cdot h_{cone} = \frac{1}{3} \left(\frac{A}{5}\right) \left(\frac{H}{2}\right) = \frac{A \cdot H}{30}. Number of cones n=VcylVcone=A⋅HA⋅H30=30n = \frac{V_{cyl}}{V_{cone}} = \frac{A \cdot H}{\frac{A \cdot H}{30}} = 30.

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