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Volume and Pi

Date: 11/10/97 at 12:00:19
From: Jake Lail
Subject: Volume and Pi

How do you find the volume of a cylinder that is 7.5mm high and has a 
diameter of 4mm? 

I haven't been able to figure out any part of this problem.

Thank You,
Jake Lail

Date: 11/12/97 at 23:02:19
From: Doctor Otavia
Subject: Re: Volume and Pi

Hi!  I assume you're talking about a cylinder where the two ends are 
parallel, resembling a straw. Let's examine what they look like, and 
figure out the formula from there.  

One way to think of a cylinder is to imagine an awful lot of circles 
stacked one on top of another. In this case the base is a circle 4mm. 
in diameter. It helps me to visualize problems, so I always imagine a 
bunch of coasters in a stack.  

We know how to find the area of a circle, which is pi*r^2. (r^2 means 
r to the 2nd power, or r squared) and we know that the radius is half 
the diameter, so we can find the area of the base.

We now know the area of one of the circles that is in the stack that 
makes up the cylinder. This is great, because we know we have a stack 
of these circles of area pi*r^2, with a stack (or cylinder) height of 
7.5mm, so what you have to do now is multiply the area of the base, 
which we know is pi*r^2 times the height, or h. The formula you get is 

  h * pi * r^2.  

All you have to do is substitute the numbers you have in your problem, 
that is, a height of 7.5mm and a diameter of 4mm (and don't forget, 
the formula asks you for the radius, which is half the diameter), into 
the formula, and you have the volume of your cylinder.  

Also, make sure you use the proper units, which in this case would be 
mm^3, or cubic millimeters, because you're multiplying the height, 
which is in mm, times the radius squared, which means mm  *mm or mm^2, 
so you end up with units of mm*mm^2, which ends up being mm^3. This 
makes sense if you think about it, because cubic millimeters are a 
unit of volume, and millimeters aren't (they just measure length), and 
millimeters squared aren't either (because they just measure area.).  

I hope this helps. Good luck!

-Doctor Otavia,  The Math Forum
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Associated Topics:
High School Geometry
High School Higher-Dimensional Geometry
Middle School Geometry
Middle School Higher-Dimensional Geometry

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