Question

Find the area of the square inside the circle if the radius of the circle is 10 inches.

Answer 1

For example, if the radius of the circle is 4,
Area of Circle = π*r²

radius = 4

π*4² = 50.2655

Area of Square = s²

s = side

Since the radius of the circle is 4, multiply it by 2 to find its diameter, which we will use to find the side of the square:

2*4 = 8

diameter of circle = 8

Since the diagonal of the square is the hypotenuse of the two triangles of the square when split, we use this formula to find the sides of the square:

hypotenuse*sinθ = side of square

θ=45°

We use 45° because it is the angle of both of the other sides of the triangle (opposite, adjacent), which both hold the same value of any side of the square; a square split in half results in two right-triangles.

Now, we have:

8sin45° = 5.656854249

side of square = 5.656854249

Now we use our area of a square formula with this newly found side:

5.656854249² = 32

Thus, Area of the square equals 32.

Now we just subtract the area of the square, from the area of the circle:

50.2655 - 32 = 18.2655

Answer: The area of the region within the circle, but outside of the square is 18 units.

I hope this helps!

Answer 2

I will let you finish