Answer:To find how rapidly the diameter of the balloon is increasing when the diameter is 1. 7 feet, we can use the formula for the volume of a sphere:.
V = (4/3)πr^3.
where V is the volume and r is the radius of the sphere. Since the diameter is twice the radius, we have:.
d = 2r.
Differentiating both sides with respect to time t, we get:.
dV/dt = 4πr^2(dr/dt).
Given that dV/dt = 3. 9 ft^3/min, and we need to find dr/dt when d = 1. 7 feet, we can substitute these values into the equation to solve for dr/dt.
Step-by-step explanation:
