Mensuration and trigonometry Study Guide

The circumference of a circle is the total distance around its outer edge. It's similar to the perimeter of other shapes, but for a circle, we use specific terminology. There are two main measurements associated with a circle that are crucial for calculating its circumference: the diameter and the radius.

The diameter (denoted by 'd') is the distance straight across the circle, passing directly through its center. The radius (denoted by 'r') is the distance from the center of the circle to any point on its edge. The key relationship between these two is that the diameter is always twice the radius (d = 2r).

To calculate the circumference (C), we use the mathematical constant pi (π). Pi is an irrational number, which means it has an infinite non-repeating decimal expansion, commonly approximated as 3.14 or 22/7. The formula for the circumference in terms of diameter is C = πd. Alternatively, if you know the radius, you can use the formula C = 2πr, which is equivalent since d = 2r.

When performing calculations, it's often more accurate to leave answers in terms of π or use the π button on your calculator. If an approximation is required, it will usually be specified (e.g., 'give your answer to 1 decimal place' or 'use π = 3.14'). Remember that the units for circumference will be the same as the units for the diameter or radius (e.g., cm, m).

The circumference of a circle is the total distance around its outer edge. It's similar to the perimeter of other shapes, but for a circle, we use a special term: 'circumference'. The key to calculating the circumference is understanding its relationship with the circle's diameter or radius, and a special mathematical constant called pi (π). Pi is an irrational number, which means its decimal representation goes on forever without repeating. For most calculations, we use an approximation like 3.14 or 22/7, or we can leave our answer in terms of π for exactness. The diameter (d) of a circle is the straight line distance across the circle, passing through its center. The radius (r) is the distance from the center to any point on the circumference. The diameter is always twice the radius (d = 2r). There are two main formulas for circumference: C = πd (pi times diameter) or C = 2πr (two times pi times the radius). These formulas are equivalent because d = 2r. When solving problems, choose the formula that is most convenient based on whether you are given the diameter or the radius. Remember to include appropriate units in your final answer, such as cm, m, or km. Precision requirements for π or rounding instructions will usually be specified in the question.