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.
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)`
= 1381.97 cm^3
The volume of the largest sphere that can be created is 1381.97 cm^3