Question

PROBLEM STATEMENT:

You are blowing air into a balloon at a rate of 4*pi/3 cubic inches per second. (The reason for this strange-looking rate is that it will simplify your algebra a little bit.)

Assume the radius of your balloon is zero at time zero.

Let r(t), A(t) and V(t) denote the radius, surface area and the volume of your balloon at time t, respectively. (Assume the thickness of the skin is zero.)

Find:

a) r'(t)

b) A'(t)

c) V'(t)

Answer 1

MY ATTEMPT OF THE PROBLEM:

I know that dV/dt = 4*pi/3 and that dV/dt = 4*pi * r^2 dr/dt, and that 4*pi/3 = 4*pi r^2 * dr/dt, which implies that 1/3 = r^2 * dr/dt.

I also found that dA/dt = 8*pi*r * dr/dt.

My issue is that I now have two equations, 1/3 = r^2 * dr/dt and dA/dt = 8*pi*r * dr/dt, but three unknowns, dr/dt, dA/dt and r.

I'm assuming that I need to find a third relationship/equation, but I cannot figure out what it is.

As always, any help would be very much appreciated!