there's a circle inside of a square like this: donlehmanjrcom/Tai%20Chi/Tai%20Chi%20Newsletters/excerpts11%20images/image001.png (add the period before the com)
the circle has a radius of 2 in and an area of 12.56 in^2
how do i find the area of the space outside the circle (the square)? there's no measurements for the square so i'm confused.
Isn't the diameter of the circle the same as one side of the square?
so
2(2) = 4
4 * 4 = 8
12.56 - 8 = 4.56 in^2 is the area?
4 * 4 does not = 8
oops
2(2) = 4
4 * 4 = 16
16 - 12.56 = 3.44 in^2
Yes, you're right.
To find the area of the space outside the circle (the square), we need to first determine the area of the square. Although there are no measurements given for the square, we can still find the area based on the given information.
Since the radius of the circle is 2 inches, we know that the side length of the square is twice the radius, or 4 inches. This is because when a square is inscribed in a circle, the diagonal of the square is equal to the diameter of the circle, and each side of the square is equal to the radius multiplied by the square root of 2.
So, the square has a side length of 4 inches.
To find the area of the square, we simply square the side length. In this case, the area of the square is 4 inches (side length) squared, which equals 16 square inches.
Now, to find the area of the space outside the circle (the square), we subtract the area of the circle from the area of the square.
The area of the circle is given as 12.56 square inches.
Thus, the area of the space outside the circle is the area of the square (16 square inches) minus the area of the circle (12.56 square inches), which equals 3.44 square inches.
Therefore, the area of the space outside the circle (the square) is 3.44 square inches.