Question 1180591
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The diameter of the semicircle is 12, so the radius is 6.<br>
The length of the curved part of the semicircle is half the circumference of a circle with radius 6: (1/2)(2pi)(6) = 6pi.<br>
When formed into a cone as described, the 6pi is the circumference of the base of the cone; the radius of the base is then (6pi)/(2pi) = 3.  The radius of the semicircle is now the slant height of the cone.<br>
Use the Pythagorean Theorem with the slant height and radius of the cone to determine the height.  Then<br>
{{{V = (1/3)(base)(height)}}}<br>