Find-the-minimum-surface-area-of-a-solid-circular-cylinder-if-its-volume-is-16pi-cm-3-leave-your-answer-in-terms-of-pi-

Question Number 23133 by tawa tawa last updated on 26/Oct/17

Find the minimum surface area of a solid circular cylinder, if its volume is

16 π {cm}^{3} (leave your answer in terms of π)

Answered by ajfour last updated on 26/Oct/17

S = 2 π r h + 2 π r^{2}

V = π r^{2} h \Rightarrow \frac{d h}{d r} = - \frac{2 V}{π r^{3}} \dots (i)

\frac{d S}{d r} = 2 π h + 2 π r \frac{d h}{d r} + 4 π r = 0

u s i n g (i), t h i s \Rightarrow

2 π h + 2 π r (- \frac{2 V}{π r^{3}}) + 4 π r = 0

\Rightarrow h = \frac{2 V}{π r} - 2 r = \frac{2 (π r^{2} h)}{π r^{2}} - 2 r

\Rightarrow h = 2 h - 2 r

o r h = 2 r

N o w V = π r^{2} h = π r^{2} (2 r) = 16 π {c m}^{3}

\Rightarrow r^{3} = 8 {c m}^{3} o r r = 2 c m

a n d h = 2 r = 4 c m

s o S = 2 π r h + 2 π r^{2}

= 2 π (3 r^{2}) = 2 π \times 12 {c m}^{2}

S = 24 π {c m}^{2} .

Commented by tawa tawa last updated on 26/Oct/17

God bless you sir .