Thread: Rate of Change Problem

Hi, I was just wondering if someone could tell me if I am doing the following problem correctly?

The vertices of a square are moving away from the centre at a rate of 2 cm/s. How fast is the area of the inscribed circle changing when the side of the square is 20 cm?

I let r=10 cm and plugged it into the derivative of the area of a circle... is this what I am supposed to do?

Thanks for any help

r - radius of inscribed circle at start
a - side of square at start;

, you spotted that well.

Now "The vertices of a square are moving away from the centre at a rate of 2 cm/s ", what that means actually?

Spoiler:

That means the diagonal of the rectangle is increasing by 2x of both sides, where x is s, as you stated

Here is the calculation of the side of the rectangle:

Spoiler:

z - the side of rectangle after s passed

Now what is r after?

Spoiler:

Finally,



Regards.