Find, the nearest tenth, the area of the region that is inside the square and outside the circle. The diameter of the circle is 14in.
I assume you are referring to a circle inscribed in a square. If not, please clarify
the diameter of the circle is the same as the side of the square, 14 in.
area of circle = 49pi
area of square = 14^2 = 196
so, the difference is 196-49pi =~ 42in^2
a+b = the absolute value a + b
10.5 in2
To find the area of the region that is inside the square and outside the circle, you first need to find the area of the square and the area of the circle, and then subtract the area of the circle from the area of the square.
1. Start by finding the area of the square. Since a square has all sides equal, and the diameter of the circle is 14 inches, we know that the side length of the square is also 14 inches.
- To find the area of a square, you need to square the length of one of its sides. In this case, 14 x 14 = 196 square inches.
2. Now, find the area of the circle. The formula to find the area of a circle is A = πr², where A represents the area and r represents the radius. Since the diameter given is 14 inches, we can calculate the radius.
- The radius is half the diameter, so the radius of the circle is 14 / 2 = 7 inches.
- Now, substitute the radius value into the formula: A = π x (7)² = π x 49 = 153.94 square inches (rounded to the nearest hundredth).
3. Finally, subtract the area of the circle from the area of the square to find the area of the region that is inside the square and outside the circle: 196 - 153.94 = 42.06 square inches.
Therefore, the area of the region that is inside the square and outside the circle, rounded to the nearest tenth, is approximately 42.1 square inches.