Firefighter Practice Exam

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How many square inches of sheet metal remain after cutting a 23.5-inch diameter circle from a 24-inch square sheet?

142.26 square inches
147 square inches
159.87 square inches
163.2 square inches

The correct answer is: 142.26 square inches

To determine the amount of sheet metal that remains after cutting out a circle from a square sheet, it is necessary to calculate the area of the square and the area of the circle, and then find the difference between the two areas. First, the area of the square sheet can be calculated using the formula for the area of a square, which is side length squared. A 24-inch square has an area of: Area of square = side × side = 24 inches × 24 inches = 576 square inches. Next, the area of the circle can be calculated using the formula for the area of a circle, which is π multiplied by the radius squared. The diameter of the circle is given as 23.5 inches, so the radius is half of that: Radius = 23.5 inches ÷ 2 = 11.75 inches. Now, plug the radius into the circle area formula: Area of circle = π × (11.75 inches)² ≈ 3.14 × 138.0625 square inches ≈ 433.67 square inches. Now, to find the remaining area of the sheet metal after the circle is cut out, subtract the area of the circle from the area of the square