Final answer:
The correct option is A). To find the value of A, use the formula for the volume of a sphere and the given rate of change of the radius to set up and solve an equation.
Step-by-step explanation:
To find the value of A, we need to use the formula for the volume of a sphere, which is V = (4/3)πr³.
We are given that the rate of change of the radius is 2 cm/min when the volume is 487 cm³.
Let's set up an equation and solve it:
(4/3)πr³ = 487
Substitute the given rate of change of the radius:
(4/3)π(2t)³ = 487
Simplify and solve for t:
8πt³ = 487
t³ = 487/(8π)
t = ∛(487/(8π))
t ≈ 2.740
Therefore, the value of A is approximately 27.40. Option A is the correct answer.