Solve Geometry Problem: Volume of Solid Swept by UXWV

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The problem involves calculating the volume of a solid formed by a rectangle UXWV with dimensions 4 inches by 3 inches, which moves perpendicularly along a diameter line YT. The circumference of circle T is given as 16π, leading to a diameter of 16 inches. This diameter represents the height of the solid created as the rectangle sweeps through space. The area of the base of the solid is 12 square inches, resulting in a total volume of 192 cubic inches. The final volume calculation confirms the solid's dimensions and the method used to derive it.
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Homework Statement


UXWV is a ractangle with the sides of 4in and 3in and the diametral line YT is perpendicular to he plane of UXWV. The Circumference of Circle T = 16 pi.. Imagine rectangle reminaing perpendicular to YT as U moves up to Y along URY.

http://img8.imageshack.us/img8/7596/mathprob.jpg

What is the volume of the solid the rectangle UXWV sweeps through??


Homework Equations


...


The Attempt at a Solution


no idea how to start...
 
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You have a rectangle with sides 4 in and 3 in and it moves perpendicularly a distance D, the diameter of the circle, creating a solid "4 in by 3 in by D in". You know the circumference of the circle is 16 pi in. What is the diameter, D, of the circle?
 
SO the formula for circumference is pi*d, thus 16pi would make the diameter 16, which will be he height of your solid, and since you are tiling the rectangles, the area formula will still be the area of the base * height, and the area of the base is 12insqrd, and so the voluma will be 192 in cubed?
 

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