Question

A spherical balloon is inflated so that it's volume is increasing at A rate of 2 m^3/sec. At what rate is the balloon's radius increasing when the radius is 7 m?

Answer 1

V=4/3 *pi *r^3 is volume of sphere
V'=4/3*pi*3r^2*r' is the rate of the volume (we are given V'=2 m^3/sec)
we want to find r' when r=7.
2=4/3*pi*3*(7^2)*r'
2=4*pi*49*r'
2=196pi*r'
2/(196pi)=r'

Answer 2

r'=1/(98pi)

Answer 3

Thank you! Could you please help me answer the newton's method question I posted earlier?