Question

A spherical balloon has radius r units.Show that the percentage increase in its volume is approximately 0.3 if its radius increases 0.1 percent.

Answer 1

we can use the formula
V = 4/3 Pi r^3

Answer 2

dV/dr = 4Pi*r^2

dV = 4 Pi * r^2 * dr

so if we increase radius by .1 percent (.001)
what do we increase volume by

Answer 3

0.3