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