Find the area of a circle

[easypeasyjeasy]

Hi!
I've been thinking a lot about this problem, but cannot find the solution. I hope you can help.

The figure shows two circles. The small circle has radius r, while the large circle has radius R.
It is stated that R = 13 and that the area of the shaded area is 25π.
a) Determine the radius r of the small circle.

 

[pka]

What is the area of the small circle?

 

[easypeasyjeasy]

What is the area of the small circle?

It is not given. All the information I’ve is already written

 

[Deleted member 4993]

It is not given. All the information I’ve is already written

What is the area of the small circle - as a function of the unknown variable 'r'?

 

[pka]

It is not given. All the information I’ve is already written

That is the whole point. The area of the large circle is \(\displaystyle 13^2\pi\)
From there what is the area of the small circle?

 

[easypeasyjeasy]

What is the area of the small circle - as a function of the unknown variable 'r'?

r is the radius for the small circle and I guess it’s an unknown variable?

 

[easypeasyjeasy]

That is the whole point. The area of the large circle is \(\displaystyle 13^2\pi\)
From there what is the area of the small circle?

It is 13^2*pi-r^2*pi
So I’ve to isolate r^2?

 

[Deleted member 4993]

It is 13^2*pi-r^2*pi
So I’ve to isolate r^2?

Yes...

That It - I suppose you meant "the shaded area"

and you are given value for that [25 * pi()]

Now solve by equating and isolating.

 

[easypeasyjeasy]

[MATH][/MATH]
so this is how I should write it or am I totally wrong? also it seems to be a quadratic equation
13^2*pi-r^*2*pi = 25*pi

 

[Dr.Peterson]

Yes, that's correct.

It's a quadratic equation, but a very simple one once you simplify it. First divide by pi ...