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Question
Hi,

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

General equation for surface area of a sphere:
a = 4πr²

Let r₀ be the initial radius of the sphere.
a₀ = 4πr₀²

Let r₁ be the new radius, r₁ = pr₀.
a₁ = 4πr₁²
= 4π(pr₀)²
= 4πp²r₀²
= (4πr₀²)p²
= a₀p²

For example, if r₁ = ½ of r₀, then a₁ = a₀(½)² = a₀(¼).

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#### Janet Yang

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