Question

What are the optimized dimensions of a cylinder that would result in a maximum volume given a surface area of 450 cm squared

Please Explain =]

Answer 1

volume =
\[\pi r^2h\] yes

Answer 2

and surface area = 2pi r^2 + 2pi rh

Answer 3

use the surface area to determine the value of one variable in terms of the other; and derive the volume

Answer 4

surface area is
\[4\pi r^2+2\pi r h=450\]

Answer 5

2(p r^2) = 2pi r^2 maybe?

Answer 6

solve second one for h, plug into first one to get an equation in one varaible

Answer 7

oh of course you are right. it is
\[2\pi r^2+2\pi r h\]

Answer 8

back to the dungeon for me

Answer 9

and take the mop with you :)

Answer 10

lets see if i can do next part right
\[h=\frac{450-2 \pi r^2}{2 \pi r}=\frac{225}{\pi r}-r\]

Answer 11

making
\[V(r)=\pi r^2 (\frac{225}{\pi r}-r)\]

Answer 12

\[V(r)=225r-\pi r^3\]

Answer 13

take the derivative, set = 0, solve for r and be done

Answer 14

i get
\[V'(r)=225-3\pi r^2\]

Answer 15

put

\[225-3 \pi r^2=0\]
\[r^2=\frac{225}{3\pi}=\frac{75}{\pi}\]

Answer 16

and therefore
\[r=\frac{5\sqrt{3}}{\sqrt{\pi}}\]

Answer 17

is your max

Answer 18

i mean it will give you the max volume

Answer 19

cool thnx

Answer 20

yw

Answer 21

that answer seems a bit contrived dontch think ;)

Answer 22

i was wondering well i hve the answer just not the wrking itss bh=9.6 cm & r= 4.8 cm

Answer 23

then its good :)

Answer 24

*its not bh it h=9.6 cm

Answer 25

kk gracias

Answer 26

thhnxx again