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# Advanced Math/Radius

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Question
G. Morning,

This is not homework.

We want to calculate the surface area of a sphere as it decreases down towards the center of the sphere.  Multiplying surface area by the radius would given an incorrect result as that would not encompass the surface area getting smaller.

Multiplying the full surface area by what  "percent of the radius"  would give a correct value ?

Thanks so much,
Anne

Answer
The formula for the surface area of the sphere is 4pir^2. This mean she surface area varies with the *square* of the radius. So if the sphere is half as large than the surface area is only 1/4 as big. So you need to multiply the full surface area by the square of the percent

80% of the original radious gives (.8)^2= 64% of the original surface area.

ETc...

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