CalcAB Related Rates

$$A = \pi r^2$$ where A is the area and r is the radius.

It represents the rate of change of area A with respect to time t.

It represents the rate of change of radius r with respect to time t.

The area of a circle increases with the square of the radius, as given by the formula $$A = \pi r^2$$ .

It will be negative, indicating that the area is decreasing over time.

Use implicit differentiation on the area formula $$A = \pi r^2$$ to relate \( \frac{dA}{dt} \) and \( \frac{dr}{dt} \).

$$V = \frac{4}{3} \pi r^3$$ where V is the volume and r is the radius.

Differentiate the volume formula with respect to r: $$\frac{dV}{dr} = 4\pi r^2$$ .

It indicates that the quantity is decreasing over time, such as the radius of a puddle shrinking.

$$\frac{dA}{dt} = 2\pi r \frac{dr}{dt}$$ .