A cylinder, a cone and a hemisphere have bases of equal radii and are of equal heights. Then the ratio of their volumes is ……… A) 3 : 1 : 2
A cylinder, a cone and a hemisphere have bases of equal radii and are of equal heights. Then the ratio of their volumes is ………
A) 3 : 1 : 2
B) 3 : 2 :1
C) 1 : 2 : 3
D) 1 : 3 : 2
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Correct option is: A) 3 : 1 : 2
Let r be the radii of cylinder, cone & hemisphere.
\(\because\) Height of hemisphere = Radius of hemisphere = r
\(\therefore\) Height of cone = Height of cylinder = r
\(\therefore\) h = r
Now, volume of cylinder : Volume of cone ; Volume of hemisphere.
= \(\pi r^2h : \frac 13 \pi r^2h : \frac 23 \pi r^3\)
= 3h : h : 2r (On dividing by \(\frac {\pi r^2}{3}\))
= 3r : r : 2r (\(\because\) h = r)
= 3 : 1 : 2 (On dividing by r)
Hence, the ratio of their volumes is 3 : 1 : 2.
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