areageometry
I have a square with sides of 10cm and I have a circle with radius of 6cm. Now I've to find the area of the circle that is inside of the square.Here is the graph
I had an idea of finding the area of the arc(90 degrees) and subtracting it from 25(100/4), but then I noticed that the area of arc would still include the areas which are outside of the square.
The circle of radius R in the square of side C is such :
$ 2 R = C$
Area of the circle $\pi R^2$ , of the square $C^2$ , and the ratio of circle on square is :
and the ratio is : $\pi \frac{R^2}{C^2} = \pi \frac{R^2}{4 R^2} = \frac{\pi}{4} $
If the area of the square is $100 cm^2$ , the circle will have an area of $\frac{\pi}{4} 100 cm^2 \approx 78.54 cm^2$
The square of side C in the circle of radius R is such :
$C^2 = R^2 + R^2$
similarly the ratio is : $\pi \frac{R^2}{C^2} = \pi \frac{R^2}{2 R^2} = \frac{\pi}{2} $
If the area of the square is $100 cm^2$ , the circle will have an area of $\frac{\pi}{2} 100 cm^2 \approx 157,08 cm^2$
You can use the Pythagoras Theorem and find the radius of the circle.
Best Answer
Hint: You can use the image to get the intuition. Also remember that a circle is defined as $x^2+y^2=r^2$