A-rostum-is-made-by-cutting-off-the-upper-part-of-a-cone-along-a-plane-parallel-to-the-base-at-2-3-up-the-height-What-fraction-of-the-volume-of-the-cone-does-the-rostum-represent-

Question Number 66751 by John Kaloki Musau last updated on 19/Aug/19

A r o s t u m i s m a d e b y c u t t i n g o f f

t h e u p p e r p a r t o f a c o n e a l o n g a

p l a n e p a r a l l e l t o t h e b a s e a t \frac{2}{3} u p

t h e h e i g h t . W h a t f r a c t i o n o f t h e

v o l u m e o f t h e c o n e d o e s t h e

r o s t u m r e p r e s e n t ?

Answered by MJS last updated on 19/Aug/19

V_{cone} = V_{1} = \frac{π}{3} r^{2} h

V_{u p p e r c o n e} = V_{2} = \frac{π}{3} {(\frac{r}{3})}^{2} \frac{h}{3} = \frac{π}{81} r^{2} h

V_{l e f t o v e r} = V_{1} - V_{2} = \frac{26 π}{81} r^{2} h

\frac{V_{1} - V_{2}}{V_{1}} = \frac{26}{27}

Commented by John Kaloki Musau last updated on 19/Aug/19

correct. thanks