sorry,if i had done any mistake,because i am new to these forums..

A cone,a hemisphere and a cylindrical stand on equal bases and have the same height.Show that their volumes are in the ratio 1:2:3.

I request you to please answer my question.

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- Oct 7th 2008, 12:26 AMrickymylvSurface areas and Volumes
sorry,if i had done any mistake,because i am new to these forums..

A cone,a hemisphere and a cylindrical stand on equal bases and have the same height.Show that their volumes are in the ratio 1:2:3.

I request you to please answer my question. - Oct 7th 2008, 12:40 AMearboth
Since there is a hemisphere involved you know that h = r.

Now use the formulae of the volumes:

$\displaystyle V_{cone}=\dfrac13\pi r^2\cdot r$

$\displaystyle V_{hemisphere}=\dfrac12 \cdot \dfrac43\pi r^2\cdot r = \dfrac23\pi r^2\cdot r$

$\displaystyle V_{cylinder}=\pi r^2\cdot r$

You'll get:

$\displaystyle V_{cone} : V_{hemisphere} : V_{cylinder} = \dfrac13 :\dfrac23 :\dfrac33 = 1 : 2 : 3$