Dimensions of a capsule An aspirin tablet in the shape of a right circular cylinder has he...

Dimensions of a capsule An aspirin tablet in the shape of a right circular cylinder has height  centimeter and radius  centimeter. The manufacturer also wishes to market the aspirin in capsule form. The capsule is to be  centimeters long, in the shape of a right circular cylinder with hemispheres attached at both ends (see the figure).

(a) If r denotes the radius of a hemisphere, find a formula for the volume of the capsule.

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(b) Find the radius of the capsule so that its volume is equal to that of the tablet.

EXERCISE