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# 3d geometry

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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.

Feb 9, 2022

#1
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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. Feb 9, 2022
#3
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The formula for the volume of a cone is:

Guest Feb 9, 2022
#4
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Oops! Something went wrong.

The formula for the volume of a cone is   V = (r2*pi*h ) / 3

r =>  radius of a cone base

h =>  perpendicular height to the cone base    (Not the slant height)

Answer #2 is correct!!!

Guest Feb 9, 2022
#2
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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.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Circle radius = 25               Sector angle = 120º

Cone slant height   sh = 25

The length of 120º arc = 162/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

Feb 9, 2022
edited by civonamzuk  Feb 9, 2022