# Surface areas and Volumes

• October 7th 2008, 01:26 AM
rickymylv
Surface 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.
• October 7th 2008, 01:40 AM
earboth
Quote:

Originally Posted by rickymylv
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.

Since there is a hemisphere involved you know that h = r.

Now use the formulae of the volumes:

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

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

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

You'll get:

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