Answer :
Answer:
(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.