Volume by Integration: Disk Method Practice Problem Solution
2. Calculate the volume of a wine glass. The outer edge is described by y = 0.5x3, and the radius at the top is 2 inches.
The wine glass looks like this:
The equation for the disk (I’ll let you sketch it in.) is:
The radius, r = x = (2y)1/3. Plug this in.
dV= p((2y)1/3)2dy = p22/3y2/3dy
We need limits. Note that the radius or x = 2 at the top. Use this to solve for y at this same point.
y = 0.5(2)3 = 4
So the equation is: