SOLUTION: A semicircle with diameter AD = 12cm is rolled to form
a cone by connecting A to D. What is the volume Of
the cone?
Algebra.Com
Question 1180591: A semicircle with diameter AD = 12cm is rolled to form
a cone by connecting A to D. What is the volume Of
the cone?
Answer by greenestamps(13215) (Show Source): You can put this solution on YOUR website!
The diameter of the semicircle is 12, so the radius is 6.
The length of the curved part of the semicircle is half the circumference of a circle with radius 6: (1/2)(2pi)(6) = 6pi.
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.
Use the Pythagorean Theorem with the slant height and radius of the cone to determine the height. Then
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