My Math Forum working out diameter of cylinder with only height and surface area

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 June 28th, 2015, 01:37 PM #1 Newbie   Joined: Jun 2015 From: england Posts: 22 Thanks: 0 working out diameter of cylinder with only height and surface area hello guys, Can you help? I need to work out the diamater of a cylinder with a height of 600mm and a total given surface area of 4m^2 which includes the two circular ends. would i need to work out the volume first or something and then find the radius and then find the diamater? They give me this equation: S = 2Ԉrh + 2Ԉr^2 anyone point me in the right direction please? greatfull for all your help.
 June 28th, 2015, 02:00 PM #2 Math Team     Joined: Jul 2011 From: Texas Posts: 3,005 Thanks: 1588 $\displaystyle A = 2\pi r^2 + 2\pi r h$ $\displaystyle 4 = 2\pi r^2 + 2\pi r (0.6)$ $\displaystyle 0 = 2\pi r^2 + 1.2 \pi r - 4$ $\displaystyle 0 = \pi r^2 + 0.6 \pi r - 2$ note that this equation is quadratic in $r$ ... use the quadratic formula $\displaystyle a = \pi$ , $\displaystyle b = 0.6 \pi$ , $\displaystyle c = -2$ $\displaystyle r = \frac{-b + \sqrt{b^2-4ac}}{2a}$ $\displaystyle d = 2r = \frac{-b + \sqrt{b^2-4ac}}{a}$ get out your calculator ... Thanks from topsquark, Mohajir and davey2015
June 28th, 2015, 02:00 PM   #3
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Quote:
 Originally Posted by davey2015 hello guys, Can you help? I need to work out the diamater of a cylinder with a height of 600mm and a total given surface area of 4m^2 which includes the two circular ends. would i need to work out the volume first or something and then find the radius and then find the diamater? They give me this equation: S = 2Ԉrh + 2Ԉr^2 anyone point me in the right direction please? greatfull for all your help.
This is a quadratic equation in r. So solve for r using the quadratic equation:
$\displaystyle (2 \pi ) r^2 + (2 \pi h) r - S = 0$

-Dan

Ah! skeeter beat me to it!

 June 28th, 2015, 02:48 PM #4 Newbie   Joined: Jun 2015 From: england Posts: 22 Thanks: 0 thank you guys, can you explain in each step what you did? just so i can learn easyer rather than just copying. great help
June 28th, 2015, 03:01 PM   #5
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Quote:
 Originally Posted by skeeter $\displaystyle A = 2\pi r^2 + 2\pi r h$ Okay this is the main sum to get total area. $\displaystyle 4 = 2\pi r^2 + 2\pi r (0.6)$ okay you added the area figure and 0.6 which is the height. $\displaystyle 0 = 2\pi r^2 + 1.2 \pi r - 4$ okay you changed the area from the subject to other side cancelling it out. why has the 2 changed to 1.2??? $\displaystyle 0 = \pi r^2 + 0.6 \pi r - 2$ why changes to 0.6 to and -2?? note that this equation is quadratic in $r$ ... use the quadratic formula $\displaystyle a = \pi$ , $\displaystyle b = 0.6 \pi$ , $\displaystyle c = -2$ $\displaystyle r = \frac{-b + \sqrt{b^2-4ac}}{2a}$ $\displaystyle d = 2r = \frac{-b + \sqrt{b^2-4ac}}{a}$ get out your calculator ...
Result i got was "8.174596669"

can you break the above down for me please?

Last edited by davey2015; June 28th, 2015 at 03:03 PM.

 June 28th, 2015, 03:30 PM #6 Member   Joined: Jun 2015 From: Casablanca Posts: 47 Thanks: 3 $d=r=\dfrac{-b+\sqrt{b^2 -4ac}}{2a}$ $=\dfrac{-0.6\pi+\sqrt{(0.6\pi)^2 -4\pi *(-2)}}{2\pi}$ $\approx 0.55241995$ Redo again the calculations to train yourself.
 June 28th, 2015, 04:28 PM #7 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 What do you need broken down? Do you know the "quadratic formula"? Do you know how to "complete the square" in a quadratic equation?
June 28th, 2015, 05:20 PM   #8
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Quote:
 Originally Posted by skeeter $\displaystyle A = 2\pi r^2 + 2\pi r h$ $\displaystyle 4 = 2\pi r^2 + 2\pi r (0.6)$ 2(0.6) = 1.2 ... $\displaystyle 0 = 2\pi r^2 + 1.2 \pi r - 4$ divide every term by 2 ... $\displaystyle 0 = \pi r^2 + 0.6 \pi r - 2$ ... use the quadratic formula $\displaystyle a = \pi$ , $\displaystyle b = 0.6 \pi$ , $\displaystyle c = -2$ $\displaystyle r = \frac{-b + \sqrt{b^2-4ac}}{2a}$ $\displaystyle d = 2r = \frac{-b + \sqrt{b^2-4ac}}{a}$ get out your calculator ...
kapish?

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