A sphere's radius expands from 1.0m to 1.1m. Using differentials, what is the change in the volume of the sphere (in m3)? The volume of a sphere is given by V=4/3∏r3.

Answer 1

V = (4/3)π r^3
dV/dr = 4π r^2
dV = 4π r^2 dr , but r = 1 , dr = .1
= 4π(1)(.1) = .4π