Differential Equations/Vol vs Area

Advertisement


Question
Hi Sir,

The volume of a sphere is 4/3 Pi r^3..the area is the differential 4Pir^2..why is this so..the first derivative is a slope..right? Thanks!!

Answer
It makes sense that dV/dr = surface area...

Think about it...if we increase the radius of a sphere by a small amount, say dr,
then the volume increases by about the surface area times the thickness of the
"extra layer" dr.  Hence, dV = 4*pi*r^2*dr ==> dV/dr=4*pi*r^2

See?

Abe

Differential Equations

All Answers


Answers by Expert:


Ask Experts

Volunteer


Abe Mantell

Expertise

Hello, I am a college professor of mathematics and regularly teach all levels from elementary mathematics through differential equations, and would be happy to assist anyone with such questions!

Experience

Over 15 years teaching at the college level.

Organizations
NCTM, NYSMATYC, AMATYC, MAA, NYSUT, AFT.

Education/Credentials
B.S. in Mathematics from Rensselaer Polytechnic Institute
M.S. (and A.B.D.) in Applied Mathematics from SUNY @ Stony Brook

©2016 About.com. All rights reserved.