SOLUTION: 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 prob

Algebra ->  Volume -> SOLUTION: 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 prob      Log On


   

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?
Answer by Edwin McCravy(20064) About Me  (Show Source):
You can put this solution on YOUR website!
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?


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=%28pi%2F3%29%28h%29%28b%5E2+%2B+ab+%2B+a%5E2%29 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%261%2F2=3%2F2

And we'll use the approximate fraction for pi which is 3%261%2F7=22%2F7

V=%28pi%2F3%29%28h%29%28b%5E2+%2B+ab+%2B+a%5E2%29

V=%28%2822%2F7%29%2F3%29%288%29%28%283%2F2%29%5E2+%2B+%283%2F2%29%281%29+%2B+%281%29%5E2%29

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

V=%28%2822%2F7%29%281%2F3%29%29%288%29%289%2F4+%2B+3%2F2+%2B+1%29

Get LCD of 4 in the parentheses on the right:

V=%2822%2F21%29%288%29%289%2F4+%2B+6%2F4+%2B+4%2F4%29

V=%28176%2F21%29%2819%2F4%29

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=%2844%2F21%29%2819%2F1%29

Multiply tops and bottoms:

V=836%2F21

V=39%2617%2F21, the fraction form

Edwin