How do i create a net for a cylinder that has a volume of 12pie cubic inches?

Question

i no what a net cylinder is but i don't know how to make it with a volume of 12pie cubic inches

Answer 1

volume for a cylinder is pi*r^2*h so r^2*h must be 12 here... r could be 2 and h is 3.

If r is 2, then the width of your rectangle on the net is 4pi.  The height is 3, and the circles have r=2

Answer 2

I assume you mean "12pi".  Because "pie" is the name of a round, baked dessert, not a number.  

Anyway, I'd need to know either the hieght or radius of the cylinder, because there are lots of different sized cylinders that have a volume of 12pi cubic units, and thus different ways to make a net.  Since V = pi * r^2 * h, that means 12pi = pi * r^2 * h, so r^2 * h = 12.  So if you know either the radius or the height, you can find the other measurement.

Once you have those, your net is a matter of cutting a rectangular piece that can wrap around the side of the can, plus a circular piece for the top and bottom, and sewing them together.  For the top and bottom pieces, just cut out  two circles of radius r.  If you unwrapped the net piece that went around the side, you'd get a rectangle whose height was h, and whose width was the circumference of the top and bottom, 2 pi r.  So cut out a rectangle of height h and width 2 pi r.

Answer 3

Volume = Area of the base * height.

Base = circle (Area = pi * r^2)

Therefore, volume = pi * r^2 * h

If you want Volume = 12*pi

then you must use r^2 * h = 12

You must make an assumption (unless one was given in your original question and not shown here).

For example, you want a cylinder where h = 2r  (height same as diameter)

12 = r^2 * 2r

2r^3 = 12

r^3 = 6

r = cube root of 6.

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In any event, you net would have a width equal to the circumference of the cylinder (2*pi*r) and a length equal to the height (h) plus r at each end (in order to take the full height and then wrap all the way to the centre);  a length of (h + 2r ).

You net would have a measurement of (h + 2r) by (2*pi*r).