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Question Number 132905 by bramlexs22 last updated on 17/Feb/21

	Answered by bobhans last updated on 17/Feb/21

	$T o t a l s u r f a c e a r e a = A = π r h + 2 h r + π r^{2} = 200 {c m}^{2}$ $h = \frac{200 - π r^{2}}{2 r + π r}$ $V o l o f b l o c k = V = \frac{1}{2} π r^{2} h$ $V = \frac{1}{2} π r^{2} (\frac{200 - π r^{2}}{2 r + π r}) = \frac{π r}{2} (\frac{200 - π r^{2}}{2 + π})$ $(a) V = \frac{π r (200 - π r^{2})}{4 + 2 π}$
	Answered by bobhans last updated on 17/Feb/21

	$(b) m a x i m u m v a l u e o f V .$ $\frac{d V}{d r} = \frac{1}{2 π + 4} \frac{d}{d r} [200 π r - π^{2} r^{3}] = 0$ $\Leftrightarrow \frac{1}{2 π + 4} [200 π - 3 π^{2} r^{2}] = 0$ $\Rightarrow r = \sqrt{\frac{200}{3 π}}$ $V_{m a x} = \frac{π (\sqrt{\frac{200}{3 π}}) (200 - π (\frac{200}{3 π}))}{2 π + 4}$ $V_{m a x} = \frac{4000 π \sqrt{2}}{(2 π + 4) \sqrt{3 π}} = \frac{2000 \sqrt{2 π}}{(π + 2) \sqrt{3}} {c m}^{3}$
	Commented by bramlexs22 last updated on 17/Feb/21

	$thanks$
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