You are blowing air into a spherical balloon at a rate of 2 cubic inches per second. Given that the radius of the balloon is 4 inches when t=4 seconds answer the following questions: (a) How fast is the radius of the balloon growing at t=4 seconds

(1/32π)in/seconds or 0.0099471839 inches per seconds.

Step-by-step explanation:

From the question, we have the following information

Rate = 2 cubic inches per second. Radius(r) = 4 inches

Time = 4 seconds

(a) How fast is the radius of the balloon growing at t=4 seconds = dr/dt

Volume of a Sphere = 4/3πr³

We solve using Differentiation

Rate = V(t) = 4/3πr(t)³

dv/dt = 2 cubic inches per second.

Radius at time(t) = 4 inches

Rate = V(t) = 4/3πr(t)³

dv/dt = 4πr(t)²× dr/dt

dv/dt = 4π(4)² × dr/dt

2 = 4π × 16 × dr/dt|t = 2

Making dr/dt the subject of the formula

dr/dt = 2/64π

dr/dt at t = 4 seconds = (1/32π)inches/seconds

= 0.0099471839 inches per seconds.

The radius of the balloon growing at t=4 seconds is growing at a rate or speed of (1/32π) inches/seconds

= 0.0099471839 inches per seconds.

150

Step-by-step explanation:

If u get it wrong sorry :(