Question
If two cylinders of equal volumes have their heights in the ratio 2 : 3, then the ratio if their radii is :
Answer: Option D
Let their heights be 2h and 3h and radii be r and R respectively
Then,
$$\eqalign{
& \pi {r^2}\left( {2h} \right) = \pi {R^2}\left( {3h} \right) \cr
& \Rightarrow \frac{{{r^2}}}{{{R^2}}} = \frac{3}{2} \cr
& \Rightarrow \frac{r}{R} = \frac{{\sqrt 3 }}{{\sqrt 2 }}\,i.e.,\sqrt 3 :\sqrt 2 \cr} $$
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Let their heights be 2h and 3h and radii be r and R respectively
Then,
$$\eqalign{
& \pi {r^2}\left( {2h} \right) = \pi {R^2}\left( {3h} \right) \cr
& \Rightarrow \frac{{{r^2}}}{{{R^2}}} = \frac{3}{2} \cr
& \Rightarrow \frac{r}{R} = \frac{{\sqrt 3 }}{{\sqrt 2 }}\,i.e.,\sqrt 3 :\sqrt 2 \cr} $$
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