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nas7232
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#1
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#1
A cylinder has radius r cm and heigt h cm.
The surface area = 250cm^2

Find it's volume
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DOJO
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#2
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(Original post by nas7232)
A cylinder has radius r cm and heigt h cm.
The surface area = 250cm^2

Find it's volume
I really hate circles
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RichE
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#3
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(Original post by nas7232)
A cylinder has radius r cm and heigt h cm.
The surface area = 250cm^2

Find it's volume
This isn't enough information to work out V - or do you want the answer in terms of r or h
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nas7232
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#4
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missed a bit out

v = 125r - (pir^3)/2

show how it is that ^^

my guess would be...

find the surface area then integrate it. But im not sure im doing it right.
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mcbcool
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I think if you do it in terms of r and h you get

Volume = (250hr)/(2h + r)
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nas7232
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but v = 125r - pir^3/2

I just don't know to get it

i guess:

surface area = 250
250 = 2pir
125 = pi r
125r = pir^2

the reason i cant do it is because i dont know the method of working out the area of the cylinder lol
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mizfissy815
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#7
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1) Πr^2 * h= V

Πr^2 + 2Πr*h =250
2) h = (250-Πr^2) / 2Πr

Sub 2) into 1)…

Πr^2 * (250-Πr^2) / 2Πr = V
r(250-Πr^2)=V
250r – Πr^3 = V
(divide by 2)
125r – (Πr^3)/2 = V
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mizfissy815
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#8
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hope that helps...area is equal= the area of a circle + circumference*height(this is the outer surface area)....Πr^2 + 2Πr*h
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nas7232
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#9
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#9
(Original post by fisfos815)
1) Πr^2 * h= V

Πr^2 + 2Πr*h =250
2) h = (250-Πr^2) / 2Πr

Sub 2) into 1)…

Πr^2 * (250-Πr^2) / 2Πr = V
r(250-Πr^2)=V
250r – Πr^3 = V
(divide by 2)
125r – (Πr^3)/2 = V
there is a mistake in your working
250r – Πr^3 = V
(divide by 2)
125r – (Πr^3)/2 = V

if you divide by two then you will get

125r – (Πr^3)/2 = V/2
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Twiglet
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#10
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Also for the surface area you need to do the area of the body - which you correctly identified as 2pirh , but then you need to add on the top AND bottom of the cylinder (Im pretty sure you only add on one end), this would make the surface area of the Cylnder:
SA = 2pirh + 2pir^2
i think thats right.....
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Twiglet
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#11
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okkk well it works if you ignore what I just said !
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Twiglet
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#12
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#12
SA: 2 pi rh + pi r^2 = 250 (when surface area excludes the top of the cylinder)
V: pi r^2 h therefore h= v/ (pi r^2)

put the rearranged V formula into the SA formula to get:
2 pi r [v/(pi r^2)] + pi r^2 = 250
cancel out that fraction:
2V / r + pi r^2 = 250
multiply by r:
2V + pi r^3 = 250r
divide by 2:
V + (pi r^3)/2 =125 r
rearrange to get answer....

viola - dont understand why surface area of cylinder would mean the side and bottom but not the top tho....
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