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June 28th, 2015, 01:37 PM   #1
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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.
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June 28th, 2015, 02:00 PM   #2
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$\displaystyle A = 2\pi r^2 + 2\pi r h$

$\displaystyle 4 = 2\pi r^2 + 2\pi r (0.6)$

$\displaystyle 0 = 2\pi r^2 + 1.2 \pi r - 4$

$\displaystyle 0 = \pi r^2 + 0.6 \pi r - 2$

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 ...
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June 28th, 2015, 02:00 PM   #3
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Quote:
Originally Posted by davey2015 View Post
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!
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June 28th, 2015, 02:48 PM   #4
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thank you guys, can you explain in each step what you did? just so i can learn easyer rather than just copying.

great help
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June 28th, 2015, 03:01 PM   #5
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Quote:
Originally Posted by skeeter View Post
$\displaystyle A = 2\pi r^2 + 2\pi r h$
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.
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June 28th, 2015, 03:30 PM   #6
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$d=r=\dfrac{-b+\sqrt{b^2 -4ac}}{2a}$

$=\dfrac{-0.6\pi+\sqrt{(0.6\pi)^2 -4\pi *(-2)}}{2\pi}$

$\approx 0.55241995$

Redo again the calculations to train yourself.
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June 28th, 2015, 04:28 PM   #7
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What do you need broken down? Do you know the "quadratic formula"? Do you know how to "complete the square" in a quadratic equation?
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June 28th, 2015, 05:20 PM   #8
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Quote:
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$\displaystyle A = 2\pi r^2 + 2\pi r h$

$\displaystyle 4 = 2\pi r^2 + 2\pi r (0.6)$

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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