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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: 2,883 Thanks: 1503 
$\displaystyle A = 2\pi r^2 + 2\pi r h$ $\displaystyle 4 = 2\pi r^2 + 2\pi r (0.6)$ $\displaystyle 0 = 2\pi r^2 + 1.2 \pi r  4$ $\displaystyle 0 = \pi r^2 + 0.6 \pi r  2$ note that this equation is quadratic in $r$ ... use the quadratic formula $\displaystyle a = \pi$ , $\displaystyle b = 0.6 \pi$ , $\displaystyle c = 2$ $\displaystyle r = \frac{b + \sqrt{b^24ac}}{2a}$ $\displaystyle d = 2r = \frac{b + \sqrt{b^24ac}}{a}$ get out your calculator ... 
June 28th, 2015, 02:00 PM  #3  
Math Team Joined: May 2013 From: The Astral plane Posts: 2,138 Thanks: 872 Math Focus: Wibbly wobbly timeywimey stuff.  Quote:
$\displaystyle (2 \pi ) r^2 + (2 \pi h) r  S = 0$ 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  
Newbie Joined: Jun 2015 From: england Posts: 22 Thanks: 0  Quote:
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  
Math Team Joined: Jul 2011 From: Texas Posts: 2,883 Thanks: 1503  Quote:
 

Tags 
area, cylinder, diamater, diameter, height, surface, working 
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