Volume by Integration

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:

                    dV= pr²dy

The radius, r = x = (2y)^1/3. Plug this in.

                    dV= p((2y)^1/3)²dy = p2^2/3y^2/3dy

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:

           

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