Question 894172
I have a problem I need help with. The problem is asking me to find the volume of a tall soft drink cup which has a top radius of 1.5, height of 8, and bottom radius of 1. The problem wants me to give the answer in fraction form?
<pre>
{{{drawing(3200/23,400,-2,2,-1.5,10,
green(line(0,8,1.5,8),line(0,0,1,0),line(0,0,0,8),arc(0,0,2,-1,0,180)),
line(-1,0,-1.5,8), line(1,0,1.5,8),locate(.3,8.5,1.5),locate(.22,.5,1),
locate(.1,4,8),
arc(0,8,3,1.5),arc(0,0,2,-1,180,360) )}}}

Weird-looking cup! That drawing is to scale.  Oh well!

The formula for the volume of a paper cup (or a lamp shade if upside down)
is found at this site:

http://calculus-geometry.hubpages.com/hub/Volume-of-a-Truncated-Cone-Conical-Frustum#

{{{V=(pi/3)(h)(b^2 + ab + a^2)}}} where a and b are the two radii, it doesn't matter which is which.
And h = the height.

Since you want fraction form, we'll change the decimal 1.5 to a fraction

{{{1.5=1&1/2=3/2}}}

And we'll use the approximate fraction for {{{pi}}} which is {{{3&1/7=22/7}}}

{{{V=(pi/3)(h)(b^2 + ab + a^2)}}}

{{{V=((22/7)/3)(8)((3/2)^2 + (3/2)(1) + (1)^2)}}}

Invert the 3 and multiply.  Simplify the parentheses on the right.

{{{V=((22/7)(1/3))(8)(9/4 + 3/2 + 1)}}}

Get LCD of 4 in the parentheses on the right:

{{{V=(22/21)(8)(9/4 + 6/4 + 4/4)}}}

{{{V=(176/21)(19/4)}}}

The 4 on the bottom of the second fraction goes into the 176 
on the top of the first fraction 44 times.  So we have:

{{{V=(44/21)(19/1)}}}

Multiply tops and bottoms:

{{{V=836/21}}}

{{{V=39&17/21}}}, the fraction form

Edwin</pre>