the volume of an enclosed cylindrical can with radius r cm and height h cm is 128000 cm^3,show that th surface area of the can is A=2pir^2+256000/r.find the value for r to minimize the surface area(state the value of r in term of pi)

Question

anonymous · Answer

give me a few minutes plz i m doing it now

anonymous · Answer

i dont know how i m going get it interms of pi but i got the answer with decimal places

anonymous · Answer

is r = 10185.9?

anonymous · Answer

the answer is cube root(256000/4pi

anonymous · Answer

ouch.. thats like 27.31

anonymous · Answer

yeah
did u get the solution for it?

anonymous · Answer

umm nopez.. i got something quite big compared to that..

anonymous · Answer

what i did was i differentiate A =2pir^2 + 256000/r and let it equal to the volume

anonymous · Answer

after that i solve for r

anonymous · Answer

hurm...
its ok :D
maybe i should try other question first
thanx for the help

anonymous · Answer

wait i think i know how do it

anonymous · Answer

give me 2 mins

anonymous · Answer

ok

anonymous · Answer

got it~~~

anonymous · Answer

Umm i am gonna write it out properly with the equations give me sometime

anonymous · Answer

ok
thanks :D

anonymous · Answer

$$\pi r^2h = 128000$$
$$r = \sqrt{\frac{ 128000 }{ \pi h }}$$
u differentiate the surface area and Substitute your r into the equation  dA/dr and let it equals zero so it will be like this..
$$ 4\pi \sqrt{\frac{ 128000 }{ \pi h }}) - \frac{ 256000 }{(\sqrt{\frac{ 128000 }{ h }})^2 }  =0$$ 

The from here u solve for h and substitute back to ur first equation r = squareroot (128000//pi h) to solve for r

anonymous · Answer

about the r interms of pi.. u need a graphic calculator that can be in standard mode to do it

anonymous · Answer

alright
thanks for the help :D

anonymous · Answer

no problemz :)