# Thread: Related Rates - Circular Plate

1. ## Related Rates - Circular Plate

Question: A thin, circular plate in a boiler is expanding so that its radius is changing 0.01 cm/s. How fast is the area of one face changing when the radius is 5cm?

Here is my working, I'm I on the right track so far?

$A=\pi r^2$

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

$\frac{dA}{dt}= 2\pi (5) \cdot 0.01$

$\frac{dA}{dt}= 0.314$ (this is for 2 plates - is this correct?)

Therefore, $\frac{0.314}{2} = 0.157 cm/s$ (is this correct?)

2. I don't believe you should have divided by 2. You started with the formula of the area of one face of the plate, so your answer is for that one face of the plate, not both.

3. Thanks for the correction NOX, is this correct now?

$A=\pi r^2$

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

$\frac{dA}{dt}= 2\pi (5) \cdot 0.01$

$\frac{dA}{dt}= 0.314$

4. Yes, but keep in mind that $\pi$ is only approximately equal to 3.14. Therefore, your answer is only an approximation (and it would be more accurate to use $\approx$ than $=$ or leave the answer as $\dfrac{\pi}{10}$).

5. Thanks a lot NOX!