A circle has a radius of 25. A circular sector, with an angle of \(120\) degrees at the center, is cut from the circle, and then rolled to form a cone. Find the volume of the cone.
+1632 The circle has radius 25, so the circumference is 50pi. Since the sector is 1/3 of the area, then the circumference is 1/3 of the total circumference. Thus the circumference of the sector is 50/3pi. Then the sector is rolled into a cone so the circumference of the base of the cone is 50/3pi. The radius of the cone is 25/3. The height of the cone is 25. Thus, the volume of the cone is 15625/27pi units^3.
+1694 A circle has a radius of 25. A circular sector, with an angle of 120 degrees at the center, is cut from the circle, and then rolled to form a cone. Find the volume of the cone.
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Circle radius = 25 Sector angle = 120º
Cone slant height sh = 25
The length of 120º arc = 162/3 pi
Cone radius r = 81/3
Cone height h = sqrt[252 - (81/3)2]
Cone volume = [pi(81/3)2 * h] / 3
Cone volume = 1714.075208
