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?


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Question Number 66751 by John Kaloki Musau last updated on 19/Aug/19
$A rostum is made by cutting off the upper part of a cone along a plane parallel to the base at (2/3) up the height. What fraction of the volume of the cone does the rostum represent?$
$A r o s t u m i s m a d e b y c u t t i n g o f f$ $t h e u p p e r p a r t o f a c o n e a l o n g a$ $p l a n e p a r a l l e l t o t h e b a s e a t \frac{2}{3} u p$ $t h e h e i g h t . W h a t f r a c t i o n o f t h e$ $v o l u m e o f t h e c o n e d o e s t h e$ $r o s t u m r e p r e s e n t ?$
	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
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