A cone, a hemisphere and a cylinder stand on equal bases and hve the same height , find the ratio - Maths - Surface Areas and Volumes

Question

A cone, a hemisphere and a cylinder stand on equal bases and hve
the same height , find the ratio of their volumes

Manish Bharti · Accepted Answer

Since cone, hemisphere and cylinder stands on same base ,their radius will be equal and height of each is also same.
$v o l u m e o f c o n e = \frac{1}{3} π r^{2} h v o l u m e o f h e m i s p h e r e = \frac{2}{3} π r^{3} = \frac{2}{3} π r^{2} h (h = r) v o l u m e o f c y l i n d e r = π r^{2} h$
Ratio of volumes is
$\frac{1}{3} π r^{2} h : \frac{2}{3} π r^{2} h : π r^{2} h = \frac{1}{3} : \frac{2}{3} : 1 = 1 : 2 : 3$

A cone, a hemisphere and a cylinder stand on equal bases and hve the same height , find the ratio of their volumes.