# Thread: a volume of a wine barrel

1. ## a volume of a wine barrel

When standing on one of its circular ends, a typical wine barrel has height 94 cm. The diameter of the barrel at the widest point is 70 cm. When the barrel is standing in this way, the curved edge of the vertical cross section (through the center of the barrel) is a parabola whose derivative is 2x/275, where x is the vertical distance from the center of the barrel. Assuming that 1 litre = 1000 cm^3, find the volume of wine that the barrel holds.

2. Originally Posted by kasiaogor

When standing on one of its circular ends, a typical wine barrel has height 94 cm. The diameter of the barrel at the widest point is 70 cm. When the barrel is standing in this way, the curved edge of the vertical cross section (through the center of the barrel) is a parabola whose derivative is 2x/275, where x is the vertical distance from the center of the barrel. Assuming that 1 litre = 1000 cm^3, find the volume of wine that the barrel holds.
let the barrel's vertical axis through its center lie on the x-axis.

using the method of disks w/r to x ...

$\displaystyle \displaystyle V = 2\pi \int_0^{47} \left(35 - \frac{x^2}{275}\right)^2 \, dx$

volume will be in cubic cm.

3. THANK YOU SO MUCH FOR THAT FAST ANSWER!!!

I just wonder, how did you get 35 - x^2/275 ???

and the other part of the question: evaluate the validity of your answer by calculating the volume of a more fundamental solid of similar dimensions... how can I do that??