Question
A spherical balloon is being inflated. Given that the volume of a sphere in terms of its radius is V(r)= 4/3 πr^3 and the surface area of a sphere in terms of its radius is S(r)= 4πr^2, estimate the rate
at which the volume of the balloon is changing with respect to its surface area when the surface area
measures 50cm cubed.
at which the volume of the balloon is changing with respect to its surface area when the surface area
measures 50cm cubed.
Answers
oobleck
dV/dt = 4πr^2 dr/dt
dS/dt = 8πr dr/dt
dV/dS = (dV/dt) / (dS/dt) = r/2
So now just find r when A = 50
dS/dt = 8πr dr/dt
dV/dS = (dV/dt) / (dS/dt) = r/2
So now just find r when A = 50