SOLUTION: Find the surface area and volume of a sphere whose great circle has a circumference of 28 meters

Question 970469: Find the surface area and volume of a sphere whose great circle has a circumference of 28 meters
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
A=4 pi * r^2
circumference=28 m
C=2pi*r
r=C/2pi
r=28/2pi or 14/pi
A= 4* pi * (14/pi)^2= 4*pi * (196/pi^2)= 784/pi, since there is one pi in the numerator and one in the denominator
A=249.55 sq m.
V=(4/3) pi r^3
=(4/3) pi* (14/pi)^3
numerator is 4*14^3*pi
denominator is 3* pi^3
=4*14^3/[3*pi^2]=10976/29.61
=370.69 m^3
The ratio of the area to the volume is 4*pi*r^2/(4/3)pi*r^3=3/r
(3/r) =3/(14/pi) =3 *pi/14 or 67.3%
Area to volume is 249.55/370.69
This is 67.3%. This doesn't prove the numbers are correct; it does show that the manipulation of each formula came up with the ratio is should.

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