Area & Circumference of Circles

Why are circles different to other 2D shapes?

• Circles Overview:
  • Circles consist of points equidistant from a central point.
  • Equidistant signifies equal distances from the center.
  • The circle's perimeter is known as its circumference.
• Understanding Pi (π):
  • π (pi) is a constant (3.14159...) that connects a circle's diameter to its circumference.
• Calculations and Precision:
  • Answers may require specific decimal places or significant figures.
  • Alternatively, exact values or answers in terms of π might be requested.
  • This topic could feature in non-calculator exam papers.

How do I work with circles?

• When working with circles, it's crucial to grasp the formulas for both the area and circumference.
• There are distinct versions of the circumference formula, so it's vital not to confuse the radius with the diameter.
• Remember the relationship between the diameter and radius: ( d = 2r). However, you can use different variables to remember the formulas.

Working with Circle Formulas

Manipulating circle formulas follows a similar process to any other mathematical formula:

• Step 1: Write Down - Jot down what you know and what you need to find out.
• Step 2: Pick Correct Formula - Choose the appropriate formula for the problem.
• Step 3: Substitute and Solve - Replace variables with known values and solve the equation.

Solved Example

Example: Find the area and perimeter of the semicircle shown in the diagram. Give your answers in terms of π.
The area of a semicircle is half the area of the full circle with the same diameter, so begin by finding the area of the full circle.
Find the radius by dividing the diameter by 2.
Ans: 

Substitute this into the formula for the area of a circle A = πr².
Leave your answer in terms of π. (This just means do not multiply by π).

Find the area of the semicircle by dividing the full area by 2.

Area = 32π cm²
The perimeter of the semicircle is made up of both the arc of the circle (half of the circumference) and the diameter of the semicircle.
Find the full length of the circumference of the circle using the formula  C space equals space 2 πr  (or C = πd).
Substitute the radius = 8 cm into the formula.
Again, leave your answer in terms of straight π.

Find the full perimeter by adding this to the length of the diameter of the circle.
Perimeter = 8π + 16 cm