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If You Took A Sphere Of A Certain Diameter, And Peeled Off A Uniform Outer Layer, Like The Peel How Do You Find Out By How Much It Would Reduce The Total Surface Area Of The Object?
 The surface area of a sphere of radius 'r' is given by:surface area = 4*pi*r^2 So if you peel of a layer, lets say of thickness r1 then the surface area equation would look as follows - 4*pi*(r-r1)^2 If you wanted to calculate the voume of a sphere it would be - 4/3*pi*r^3, in this case 4/3*pi*(r-r1)^3 |
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by
Raimi  30 Jun 2008 18:31 |
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Raimi is correct that the new area of a sphere of radius r with a layer of thickness t peeled off is 4*pi*(r-t)^2. So, the decrease in the area of the sphere is 4*pi*(r^2-(r-t)^2) = 4*pi*(2rt-t^2) = 4*pi*t*(2*r-t). If r is enough larger than t so that 2*r-t is approximately 2*r, then the reduction in area is approximately 8*pi*r*t. 
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