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().

Advanced Math

All Answers

Answers by Expert:

Ask Experts


Janet Yang


I can answer questions in Algebra, Basic Math, Calculus, Differential Equations, Geometry, Number Theory, and Word Problems. I would not feel comfortable answering questions in Probability and Statistics or Topology because I have not studied these in depth.


I tutor students (fifth through twelfth grades) and am a Top Contributor on Yahoo!Answers with over 24,000 math solutions.

Co-author of An Outline of Scientific Writing: For Researchers With English as a Foreign Language

I have a Bachelor's degree in Applied Mathematics from the University of California at Berkeley.

Past/Present Clients
George White Elementary School. Homework Help program at the Ridgewood Public Library, Ridgewood, NJ. Individual students.

©2016 All rights reserved.