Chapter 8, Problem 110IAE

Interpretation Introduction

Interpretation:

The volume, dv, of a thin spherical shell of a radius r and thickness dr is 4pr²dr should be proven.

Concept introduction:

The volume of a sphere radius r= $\frac{4}{3}\pi r^3$

Volume of a sphereradius r and thickness dr = $\frac{4}{3}\pi {\left(r+dr\right)}^3$

Volume,dv, of a thin spherical shellradius r and thickness dr = $\left(\text{Volume of a sphere radius }r\text{ and thickness }dr\right)\text{-}\left(\text{Volume of a sphere radius }r\right)$

${(a+b)}^3=a^3+3a^{2}b+3a{b}^2+b^3$