The base of a solid is bound by y=4-x^1/2, the x-axis, and the y-axis. Cross sections perpendicular to the x-axis are squares. Find the volume.

Answer 1

This is a Calculus problem, not an Algebra 2 problem.

The x-y region defined by the problem is the base of a solid made up of continuous squares rising in the z-axis direction (out of the page). To find the volume of the solid we must integrate the continuously changing value of the function squared since the cross sections are squares. The boundaries of integration are x=0 (y-axis) and x=16 (where the function crosses the x-axis)

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V=∫(4-√x)²dx = 128/3 exaclty.

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