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No 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

Hey Anne,

How do you initially calculate the surface area of the sphere? The surface area of a sphere of radius r is given by A(r)=4πr². Hence the area decreases quadratically with the radius. So if the radius of the sphere decreases (or increases, even) to a fraction x of its original value, then we will have:

A(xr)=4π(xr)²=x²4πr²=x²A(r)

I hope this answers your question.

Best of luck!

Azeem

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