The volumes of a cylinder and a cone are in the ratio 3: 1. Find their diameters and then compare them when their heights are equal. |
A) Diameter of cylinder = Diameter of cone
B) Diameter of cylinder > Diameter of cone
C) Diameter of cylinder < Diameter of cone
D) Diameter of cylinder = 2 times of diameter
Correct Answer: A
Solution :
Let radii of cylinder and cone be \[{{r}_{1}}\] and \[{{r}_{2}}\]respectively. |
Then, \[\frac{\pi r_{1}^{2}h}{\frac{1}{3}\pi r_{2}^{2}h}=\frac{3}{1}\]\[\Rightarrow \]\[\frac{3r_{1}^{2}}{r_{2}^{2}}=\frac{3}{1}\]\[\Rightarrow \]\[{{r}_{1}}={{r}_{2}}\] |
\[{{d}_{1}}={{d}_{2}}\] |
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