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 June 28th, 2015, 02:37 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, 03:00 PM #2 Math Team   Joined: Jul 2011 From: Texas Posts: 3,101 Thanks: 1677 $\displaystyle A = 2\pi r^2 + 2\pi r h$ $\displaystyle 4 = 2\pi r^2 + 2\pi r (0.6)$ $\displaystyle 0 = 2\pi r^2 + 1.2 \pi r - 4$ $\displaystyle 0 = \pi r^2 + 0.6 \pi r - 2$ 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, 03:00 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, 03:48 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, 04:01 PM   #5
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 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 04:03 PM. June 28th, 2015, 04:30 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, 05:28 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, 06:20 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? Tags area, cylinder, diamater, diameter, height, surface, working Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post stgeorge Geometry 8 June 7th, 2015 09:42 PM mathsheadache Algebra 5 October 20th, 2014 08:38 PM Thepiman Calculus 2 May 9th, 2014 07:16 AM akbnayanar Algebra 3 July 13th, 2012 10:48 AM manich44 Algebra 9 October 27th, 2009 03:15 AM

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