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Sample Question 7:
Step 1: Calculate the area of the square. Since the side length of the square is 10, the area is .
Step 2: Calculate the area of the circle. The formula for the area of a circle is , where is the radius, so the area is .
Step 3: Realize that exactly 1/4 of the circle lies inside the square.
Step 4: The correct area of the union of the regions enclosed by the square and the circle excludes the quarter of the circle that is inside the square, so we subtract 1/4 of the circle's area from the total circle's area, resulting in .
Step 5: Add the area of the square and the adjusted area of the circle together to get the total area, . This corresponds to answer choice B.
A square has sides of length 10, and a circle centered at one of its vertices has radius 10. What is the area of the union of the regions enclosed by the square and the circle?
Answer Keys
Question 7: BSolutions
Question 7Step 1: Calculate the area of the square. Since the side length of the square is 10, the area is .
Step 2: Calculate the area of the circle. The formula for the area of a circle is , where is the radius, so the area is .
Step 3: Realize that exactly 1/4 of the circle lies inside the square.
Step 4: The correct area of the union of the regions enclosed by the square and the circle excludes the quarter of the circle that is inside the square, so we subtract 1/4 of the circle's area from the total circle's area, resulting in .
Step 5: Add the area of the square and the adjusted area of the circle together to get the total area, . This corresponds to answer choice B.