If a cylinder and cone have bases of equal radii and are equal heights, then the ratio of their volumes is A) 1 : 3
If a cylinder and cone have bases of equal radii and are equal heights, then the ratio of their volumes is
A) 1 : 3
B) 2 : 3
C) 3 : 1
D) 3 : 2
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Correct option is: C) 3 : 1
Let the radii of both cylinder and cone be r
and the heights of both cylinder and cone be h.
\(\therefore\) Volume of cylinder is \(V_1 = \pi r^2h\)
Volume of cone is \(V_2 = \frac 13 \pi r^2 h\).
Ration of their volumes = \(\frac {V_1}{V_2}\) = \(\frac {\pi r^2h}{\frac 13 \pi r^2h}\) =\(\frac 31\) = 3 : 1
Hence, the ratio of their volumes is 3:1.
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