Advanced Math/Radius



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,

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

Let r₀ be the initial radius of the sphere.
a₀ = 4πr₀

Let r₁ be the new radius, r₁ = pr₀.
a₁ = 4πr₁
 = 4π(pr₀)
 = 4πpr₀
 = (4πr₀)p
 = a₀p

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

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Janet Yang


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