Optimization; cylinder inside sphere

$Go Back$		Math Help Forum > University Math Help > Calculus
$Reload this Page$ Optimization; cylinder inside sphere

$Reply$

Thread Tools

Display Modes

$Old$ October 13th, 2009, 04:53 PM

$Tclack's Avatar$

Tclack $Tclack is offline$

Newbie

Join Date: Oct 2009

Location: No permanant location.

Posts: 15

Country:

Thanks: 6

Thanked 1 Time in 1 Post

$Tclack is on a distinguished road$

$Default$ Optimization; cylinder inside sphere

Find the dimensions(r and h) of the right circular cylinder of greatest Surface Area that can be inscribed in a sphere of radius R.

my work so far

$SA=2\pi r^2+2\pi rh$

$r^2 + (\frac{h}{2})^2 = R^2$

$h=2\sqrt{R^2-r^2}$

$SA=2\pi r^2+4\pi r\sqrt{R^2-r^2}$

$\frac{dSA}{dr}=4\pi r+4\pi (\sqrt{R^2-r^2}+\frac{-2r^2}{2\sqrt{R^2-r^2}})$

I tried setting that equal to zero, but I wasn't coming up with the right answer

The answer in the book(not mine): $r=\sqrt{\frac{5+\sqrt{5}}{10}}R$
$h=2\sqrt{\frac{5-\sqrt{5}}{10}}R$

Can anyone see my error, or did I make one?

Last edited by Tclack; October 13th, 2009 at 04:54 PM. Reason: clarification

$Reply With Quote$

$Reply$

Tags

cylinder, max, min, optimization, sphere

« Trouble with Tangents | Top | Related Rates problem! (Why can they bo so difficult?) »

Thread Tools
$Show Printable Version$ Show Printable Version $Email this Page$ Email this Page
Display Modes
$Linear Mode$ Linear Mode $Hybrid Mode$ Switch to Hybrid Mode $Threaded Mode$ Switch to Threaded Mode

Posting Rules
You may not post new threads You may not post replies You may not post attachments You may not edit your posts BB code is On Smilies are On [IMG] code is On HTML code is Off Trackbacks are Off Pingbacks are Off Refbacks are Off

Forum Jump

All times are GMT -7. The time now is 07:34 AM.

Math Help Forum is a community of maths forums with an emphasis on maths help in all levels of mathematics.
Register to post your math questions or just hang out and try some of our math games or visit the arcade.