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A cone, a hemisphere and a cylinder stand on equal bases and have the same height. The ratio of their respective volume is
Answer & Solution
Correct Answer:
Option
A
In this case height of cylinder and cone is equal to the radius of hemisphere
⇒ h = r
Ratio of volumes
\[\begin{array}{*{20}{c}} {}&{{\text{Cone}}}&{}&{{\text{Hemisphere}}}&{}&{{\text{Cylinder}}} \\ = &{\frac{1}{3}\pi {r^2} \times r}&:&{\frac{2}{3}\pi {r^3}}&:&{\pi {r^2} \times r} \\ = &1&:&2&:&3 \end{array}\]
⇒ h = r
Ratio of volumes
\[\begin{array}{*{20}{c}} {}&{{\text{Cone}}}&{}&{{\text{Hemisphere}}}&{}&{{\text{Cylinder}}} \\ = &{\frac{1}{3}\pi {r^2} \times r}&:&{\frac{2}{3}\pi {r^3}}&:&{\pi {r^2} \times r} \\ = &1&:&2&:&3 \end{array}\]
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