Firefighter Practice Exam

If you need to calculate the area of a circular cut from a square sheet of metal, which formula is required?

1. Area = π × R²

2. Area = Length × Width

3. Area = 2 × π × R

4. Area = 4 × R

The correct answer is: Area = π × R²

To determine the area of a circular cut from a square sheet of metal, the appropriate formula to use is the one that relates to the properties of a circle. The formula for the area of a circle is Area = π × R², where R represents the radius of the circle. This formula derives from the fundamental principles of geometry involving circles, where π (pi) is a constant (approximately 3.14) that represents the ratio of the circumference of a circle to its diameter. The area calculated using this formula gives the total space covered by the circular shape, which is essential when assessing how much of the material will be used or removed from the square sheet. Other provided formulas relate to different shapes or measurements; for instance, the formula for the area of a rectangle is Length × Width, which does not apply when calculating the area of a circle. Similarly, the 2 × π × R formula calculates the circumference (the distance around the circle), and the formula 4 × R does not represent any standard geometric area calculation relevant to circles. Therefore, using the correct formula is critical for accurately determining the area of the circular cut.