A circle fits within a square with side lengths of 12 inches. What is the approximate area of the shaded region between the square and the circle? (Use 3.14 for π and round to the nearest whole number.) Options: - 31 in² - 69 in² - 106 in² - 125 in²
Mathematics · Middle School · Thu Feb 04 2021
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To find the area of the shaded region between the square and the circle, we first calculate the area of the square and then the area of the circle, and subtract the area of the circle from the area of the square.
Step 1: Calculate the area of the square. The formula for the area of a square is side length squared. So, if the side of the square is 12 inches, the area is: Area_square = side * side = 12 inches * 12 inches = 144 square inches
Step 2: Calculate the area of the circle. Since the circle fits perfectly within the square, its diameter is equal to the side length of the square, which is 12 inches. Therefore, the radius (r) of the circle is half the diameter, which is 6 inches. The formula for the area of a circle is πr^2, where π can be approximated as 3.14. So, the area is: Area_circle = π * r^2 = 3.14 * 6 inches * 6 inches = 3.14 * 36 = 113.04 square inches
When we round this to the nearest whole number, we get approximately 113 square inches.
Step 3: Subtract the area of the circle from the area of the square to find the area of the shaded region. Area_shaded = Area_square - Area_circle = 144 square inches - 113 square inches = 31 square inches
So, after rounding the area of the shaded region to the nearest whole number, it is approximately 31 square inches.
Therefore, the correct answer is: 31 in².