finding the 2:1 ratio height and radius of a cylinder using the volume

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tracer123

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Hello everyone.

I'm trying to find the answer to finding the radius and height of a cylinder when only knowing the volume with the ratio 2:1 height to diameter, can anyone help?.
 
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tracer123 said:
I trying to find the answer to finding the radius and height of a cylinder when only knowing the volume with the ratio 2:1 height to radius,
Click to expand...
What have you tried so far? For instance, you listed the relevant formula(s) for cylinders, you created the ratio equation with the relevant variables and given numbers, plugged from this into the formula you picked, and... then what?

Please be complete, including the volume value you were given. Thank you! ;)
 
The volume of the cylinder is 9.16m3.

I have to find the radius and height of the cylinder with the ratio of the diameter to the height of 1:2.

I've tried the formulae on the previous post but still getting a bit stuck, can you help?

 
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Stapel asked you:

For instance, you listed the relevant formula(s) for cylinders,
Click to expand...

What is the FORMULA for Volume of a cylinder?

For example, the formula for volume of cube with side 's' = s^3

So

What is the FORMULA for Volume of a cylinder (whose diameter of the base is "D" and height is "H"?
 
Subhotosh Khan said:
Stapel asked you:



What is the FORMULA for Volume of a cylinder?

For example, the formula for volume of cube with side 's' = s^3

So

What is the FORMULA for Volume of a cylinder (whose diameter of the base is "D" and height is "H"?
Click to expand...


The formulae I'm using is, Pir^2xh = 9.16m3
 
tracer123 said:


The volume of the cylinder is 9.16m3.

with the ratio a of the diameter to the height of 1:2, now have to find the radius and the height.

I've tried once of the previous post formulae and are still a bit stuck, can you help?.
Click to expand...


V = 9.15m3 = PiR^2h making h = 9.16 - PiR^2
A = PiR^2 + =2PiRh
Substituting for h yields A = PiR^2 + 100PiR - 2Pi^2R^3
The first derivitive yields dA/dR = 2PiR + 18.32Pi - 6Pi^2R^2 = 0
Simplifying, 6PiR^2 - 2R - 18.32 = 0
Using the quadratic formula,

(2+/- sqrt(2-4x6Pix-18.31) / 12Pi.

Getting 0.91963....
and 1.0257.....

but once I put them back in to check if their correct I'm still out by 0.65 on the original volume so I guess I'm out somewhere along the line.
 
tracer123 said:
Hello everyone.

I'm trying to find the answer to finding the radius and height of a cylinder when only knowing the volume with the ratio 2:1 height to diameter, can anyone help?.
Click to expand...

π * r^2 * h = 9.16 ...... d = h/2 → r = h/4

r^3 = 9.16 /(4*π)

r = 0.89971 = 0.9 → h = 3.6

check

V = π * (.9)^2 * 3.6 = 9.160884 .............. checks
 
Subhotosh Khan said:
π * r^2 * h = 9.16 ...... d = h/2 → r = h/4

r^3 = 9.16 /(4*π)

r = 0.89971 = 0.9 → h = 3.6

check

V = π * (.9)^2 * 3.6 = 9.160884 .............. checks
Click to expand...


Thank you for your help.

Just a quick question, how did you get the 0.89971, I've just gone through your working out dividing 9.16 by 4*Pi and it comes out as 0.72892......

could you please explain how you got that figure, thank you.
 
tracer123 said:
Thank you for your help.

Just a quick question, how did you get the 0.89971, I've just gone through your working out dividing 9.16 by 4*Pi and it comes out as 0.72892......

could you please explain how you got that figure, thank you.
Click to expand...

Did you use paper and pencil and worked through the whole calculation - or just stared at the screen??!!

r^3 = 0.72892

r = (0.72892)^(1/3) = 0.899917 ...... Got it!!
 
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