# Math Help - Related rates problem

1. ## Related rates problem

Hi I've got two related rates problem that I didn't manage to solve.

The first one is:
The area of a square is decreasing at 2 ft^2/s. How fast is the side length changing when it it 8 ft?

The second one is:
The area of a circle is decreasing at a rate of 2cm^2/min. How fast is the radius of the circle changing when the area is 100 cm^2?

I guess the problems are of the same type. Thankful for all the help I can get

2. ## Re: Related rates problem

$\frac{d}{dt}\left(A = s^2\right)$

$\frac{dA}{dt} = 2s \cdot \frac{ds}{dt}$

sub in your given values and determine the value of $\frac{ds}{dt}$

now do the same with the circle problem

3. ## Re: Related rates problem

I managed to solve the first problem but not the second one. There is a difference between them. In the first they are asking for the side length over time when the side is 8ft, while they in the second one are asking for the radius over time when the area is 100 cm^2.

4. ## Re: Related rates problem

Originally Posted by Benji

I managed to solve the first problem but not the second one. There is a difference between them. In the first they are asking for the side length over time when the side is 8ft, while they in the second one are asking for the radius over time when the area is 100 cm^2.
come on, Benji ... you have to think a little bit.

$\frac{d}{dt}\left(A=\pi r^2\right)$

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

you were given the rate of change of the area, $\frac{dA}{dt}$

you were also given the area ... can you not calculate the value of the radius when $A = 100 \, cm^2$ ?

sub in those values and determine the value of $\frac{dr}{dt}$