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.

Guest Feb 9, 2022

#1**0 **

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. **

proyaop Feb 9, 2022

#2**0 **

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 = 16^{2}/_{3 }pi

Cone radius r = 8^{1}/_{3}

Cone height h = sqrt[25^{2} - (8^{1}/_{3})^{2}]

Cone volume = [pi(8^{1}/_{3})^{2} * h] / 3

**Cone volume = 1714.075208**

civonamzuk Feb 9, 2022