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1. A solid is constructed so that it has a circular base of radius r centimeters and every plane section perpendicular to a certain diameter of the base is a square, with a side of the square being a chord of the circle.

a. Find the volume of the solid.
b. If the solid describe expands so that the radius of the base increases at a constant rate of ½ centimeters per minute, how fast is the volume changing when the radius is 4 centimeters?

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