I need finding the volume of the solid of revolution (a cup), convert the volume to ounces and having the calculation be a close approximate to the measured ounces.

I'm using the equation of the line but I'm not getting the results I'm looking for. I know the volume of the solid (a cup which is 16 oz) but my calculation are not coming close to it.

I was told to use the equation of the line to solve it but I'm not not getting the result I'm looking for.

How I'm finding the volume of the cup:

Cut the cup in half and trace that half to a graphing papaper mark the end points and calculate volume.

My calculations:

equation of the line

y = -1/4x + 15/2

volume of the solid of revolution: my calculations

Edit: What I was doing wrong

Is not that my calculation were wrong is just that went

1) I cut the cup in half, that half was a couple cm bigger than other half

2) went I traced half cup to the graph paper it wasn't properly center

3) I traced the end points from the top to the bottom but the bottom was intended about 0.5cm inside


Got new a cup and fixed the problems above and I'm getting a better approximation of 16.364oz


Each point in the graph is a centimeter


  • $\begingroup$ There are many curves joining two points. Which curve were you told to use? $\endgroup$ – Joonas Ilmavirta Nov 6 '14 at 7:47
  • $\begingroup$ Come on, Joonas! Surely this is a regular cup, and he's supposed to use a line. The volume looks right. The cup is quite large. Over a liter, so more than a quart. Close to 40 fluid ounces. Looks like a misplaced decimal point? $\endgroup$ – Jyrki Lahtonen Nov 6 '14 at 7:51
  • $\begingroup$ Here's a theory. You were told that the bottom of the cup is a circle with diameter 4 centimeters and the top has a diameter of 7 centimeters. But the volume you calculated is that of a cup, where those are the RADII! That cup is about 6 inches wide at the top! If you correct for this mistake you get something close to 10 oz. Oh, and there's an error in your pic. You should have flipped the sign of the $y$-coordinate instead of the $x$. $\endgroup$ – Jyrki Lahtonen Nov 6 '14 at 8:01
  • $\begingroup$ The cup sized is a regular styrofoam cup I measured the volume myself it hold 16oz(2 cups). I graphed the cup to a graph paper where each four squares measures a cm. $\endgroup$ – PLOW Nov 6 '14 at 8:03
  • $\begingroup$ I think I just found I was doing wrong. I cut the cup in half and when I traced the cup to the graph paper I flatten out the cup thus extending it. $\endgroup$ – PLOW Nov 6 '14 at 8:17

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