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A sphere is to be formed with a sheet of plastic that is 600 cm^2 in area. What is the...

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lxsptter | Student, Undergraduate | Valedictorian

Posted April 6, 2013 at 7:06 PM via web

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A sphere is to be formed with a sheet of plastic that is 600 cm^2 in area. What is the area of the largest sphere that can be created.

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted April 6, 2013 at 7:15 PM (Answer #1)

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A sphere of radius r has a volume `(4/3)*pi*r^3` and the area is `4*pi*r^2` . The sheet of plastic with which the sphere has to be created is 600 cm^2 in area.

If the radius of the largest sphere created is r, `4*pi*r^2 = 600`

=> `r^2 = 150/pi`

=> `r = sqrt(150/pi)`

The volume of this sphere is `(4/3)*pi*(sqrt(150/pi))^3`

= `(4/3)*pi*150/pi*sqrt (150/pi)`

= `200*sqrt(150/pi)`

= 1381.97 cm^3

The volume of the largest sphere that can be created is 1381.97 cm^3

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