National Occupational Competency Testing Institute (NOCTI) Carpentry Practice Exam

Which shape has the formula A = πr² for calculating area?

1. Square

2. Rectangle

3. Circle

4. Triangle

The correct answer is: Circle

The area formula A = πr² is specifically for calculating the area of a circle, where "r" represents the radius of the circle. In this formula, π (pi) is a mathematical constant approximately equal to 3.14, which relates the circumference of a circle to its diameter. A circle is defined as a set of points in a plane that are at a constant distance (the radius) from a central point (the center). The formula captures this relationship, demonstrating how the area increases as the radius increases. Understanding this concept is essential in carpentry and construction, as circles are often present in various architectural elements, such as arches, holes, or circular tables. Other shapes like squares, rectangles, and triangles have different area formulas: a square's area is calculated as side length squared, a rectangle's area is length multiplied by width, and a triangle's area is (base × height) / 2. This differentiation is crucial in accurately performing calculations relevant to carpentry and construction projects.