the area of a circle increases at a rate of 4 cm²/s. a. how fast is the radius changing when the radius is 3…

the area of a circle increases at a rate of 4 cm²/s. a. how fast is the radius changing when the radius is 3 cm? b. how fast is the radius changing when the circumference is 2 cm? a. write an equation relating the area of a circle, a, and the radius of the circle, r. a = πr² (type an exact answer, using π as needed.) differentiate both sides of the equation with respect to t. da/dt = 2πr dr/dt (type an exact answer, using π as needed.) when the radius is 3 cm, the radius is changing at a rate of (type an exact answer, using π as needed.)

the area of a circle increases at a rate of 4 cm²/s. a. how fast is the radius changing when the radius is 3 cm? b. how fast is the radius changing when the circumference is 2 cm? a. write an equation relating the area of a circle, a, and the radius of the circle, r. a = πr² (type an exact answer, using π as needed.) differentiate both sides of the equation with respect to t. da/dt = 2πr dr/dt (type an exact answer, using π as needed.) when the radius is 3 cm, the radius is changing at a rate of (type an exact answer, using π as needed.)

Answer

Explanation:

Step1: Identify given values

We know that $\frac{dA}{dt}=4\ cm^{2}/s$ and $r = 3\ cm$. The formula for the rate - of - change of the area of a circle is $\frac{dA}{dt}=2\pi r\frac{dr}{dt}$.

Step2: Solve for $\frac{dr}{dt}$

We can re - arrange the formula $\frac{dA}{dt}=2\pi r\frac{dr}{dt}$ to solve for $\frac{dr}{dt}$. So, $\frac{dr}{dt}=\frac{\frac{dA}{dt}}{2\pi r}$.

Step3: Substitute values

Substitute $\frac{dA}{dt} = 4$ and $r = 3$ into the formula for $\frac{dr}{dt}$. Then $\frac{dr}{dt}=\frac{4}{2\pi\times3}=\frac{2}{3\pi}\ cm/s$.

Answer:

$\frac{2}{3\pi}\ cm/s$