Final answer:
When each side of a square is increasing at a rate of 4 cm/s and the side length is 10 centimeters, the area of the square is changing at a rate of 80 cm^2/s.
Step-by-step explanation:
To find how fast the area is changing, we need to use the formula for the area of a square, which is A = s^2, where A is the area and s is the side length.
Since the side length is increasing at a rate of 4 cm/s, we can find how fast the area is changing by taking the derivative of the area formula with respect to time.
The derivative of A with respect to t is dA/dt = 2s(ds/dt), where dA/dt represents the rate of change of the area, s is the side length, and ds/dt is the rate of change of the side length.
Plugging in the given values, we have dA/dt = 2(10)(4) = 80 cm^2/s.
Therefore, the area is changing at a rate of 80 cm^2/s when each side is 10 centimeters.