You are blowing air into a spherical balloon at a rate of 43cubic inches per second. (The reason for this strange looking rate is that it will simplify your algebra a little.) Assume the radius of your balloon is zero at time zero. Letr(t),A(t), andV(t) denote the radius, the surface area, and the volume of your balloon at timet, respectively. (Assume the thickness of the skin is zero.) All of your answers below are expressions int:

Calculate:

r'(t)= inches per second

A'(t)= square inches per second

V'(t)= cubic inches per second

Hint:The surface areaAand the volumeVof a sphere of radiusr are given by:

A=4pi(r^2) V=(4pi(r^3))/3