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This is a question that i was not able to solve, help about it is highly appreciated.

The radii of the bases of a cylinder and a cone are 3:4 and their heights are in the ratio 2:3, what is the ratio of their volumes?

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up vote 1 down vote accepted

You have a cylinder with height $h_1$ and radius of base $r_1$. Then the volume is $V_1 = h_1\pi r_1^2$.

You have a cone with height $h_2$ and radius of base $r_2$. The volume is $V_2 = \frac{1}{3}h_2\pi r_2^2$

Now you are told that $$\begin{align} r_1 &= \frac{3}{4}r_2\quad\text{and} \\ h_1 &= \frac{2}{3}h_2. \end{align} $$ Use this to find $$ \frac{V_1}{V_2}. $$

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Slightly incorrect - aayush is told that the ratio of the radii of the bases is 3/4. So it should be $B_1 = (3/4)^2 B_2$. – Glen O Mar 22 '13 at 14:32
That is, unless it's a typo. – Glen O Mar 22 '13 at 14:32
@GlenO: You are right. I misread the question. I updated the answer. – Thomas Mar 22 '13 at 14:43

since you have just to compute the ratio of their volumes and you have the ratio of the bases and heights, you may just choose convenient values for the latter.

Take a cylinder with base 3 cm and height 2 cm and a cone with base 4 cm and height 3 cm, and do the math.

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