Cone, a hemisphere and a cylinder stand on equal bases and have the same height. The ratio of their volumes are:
Solution
Correct Answer: Option B
Since the Cone, hemisphere and cylinder have same radius and same height
Volume of the cone is given by \(= {\rm{\;}}\frac{1}{3}{\rm{\pi }}{{\rm{r}}^2}{\rm{h}}\)
Volume of the hemisphere is given by \(= \frac{2}{3}{\rm{\pi }}{{\rm{r}}^3}\)
Volume of the cylinder is given by = πr2h
∴ Ratio of their volumes = Volume of the cone: Volume of the hemisphere: Volume of the cylinder
∴ Ratio of their volumes \(= {\rm{\;}}\frac{1}{3}{\rm{\pi }}{{\rm{r}}^2}{\rm{h\;}}:{\rm{\;}}\frac{2}{3}{\rm{\pi }}{{\rm{r}}^3}:{\rm{\pi }}{{\rm{r}}^2}{\rm{h\;}}\) [∵ r = h]
⟹ Ratio of their volumes \(= {\rm{\;}}\frac{1}{3}{\rm{\;}}:{\rm{\;}}\frac{2}{3}:1 = 1:2:3\)
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