Find the volume of the solid whose base is the region bounded by the graphs of y=x^3,x=1, and the x-axis, and whose cross sections perpenditular to the x-axis are semicircles.

What would be the radius in this case?

I thought it would just be x^3, but others are saying (x^3)/2. Please help me!

If you rotate around y=0, the x axis, the outer radius is x^3, but note the rotation is only half a circle. If you do a rotational volume based on average radius, it is x^3/2. I would never do it that way, but some do.

There are a number of ways to do this.

I don’t quite understand what you mean by “based on average radius”

Dont do it that way if you don’t understand centroids.

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