Question

a circle is inside a square as seen in the figure:

the radius of the circle is increasing at a rate of 3 meters per hour and the sides of the square are increasing at a rate of 2 meters per hour. when the radius is 2 meters, and the sides are 20 meters, how fast is the area between the circle and square changing? round the results to two decimals.

the rate of change of the area enclosed between the circle and the square is square meters per hour.

Explanation:

Define the area equation

$$ A = x^2 - \pi r^2 $$

Differentiate with respect to time

$$ \frac{dA}{dt} = 2x \frac{dx}{dt} - 2\pi r \frac{dr}{dt} $$

Substitute given values and calculate

$$
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$$

Answer:

The rate of change of the area enclosed between the circle and the square is <blank>42.30</blank> square meters per hour.