Lesson 2: Area - Area of Circles

   Constructing Knowledge

Recall that the formula for the area of a circle is:

\(\begin{align} \text{Area}_{\text{circle}}&=\pi\times \text{radius}\times \text{radius} \\ \\ &=\pi\times \text{radius squared} \\ \\ \text{A}_{\text{circle}}&=\pi r^2 \\ \end{align}\)

When using a formula to calculate area, follow these basic steps:

  1. State the formula being used to solve the problem.
  2. Substitute known values for the variables.
  3. Solve for the unknown (remember to include proper squared units in your answer).

Remember that with all area calculations, all dimensions must be in the same unit of measure prior to substituting their values into the formula.

Solution


A video demonstrating calculating the area of a circle is provided.



EXAMPLE 1

Determine the area of a circle with a radius of 10 feet. Round your answer to the nearest tenth of a square foot.

Solution


\(\begin{align} \text{A}_{\text{circle}}&=\pi r^2 \\ \\ &=\pi\times 10^2 \\ \\ &=\pi\times 10\,\text{ft}\times 10\,\text{ft} \\ \\ &=314.2\,\text{ft}^2 \end{align}\)

The area of the circle is 314.2 ft2.

If your calculator does not have the π key, you may use 3.14 for pi in your calculations.

EXAMPLE 2

Determine the radius of the circle shown. Round your answer to the nearest tenth of a metre.

Solution


\(\begin{align} \text{A}_{\text{circle}}&=\pi r^2 \\ \\ 120\,\text{m}^2&=\pi\times r^2 \\ \\ \frac{120\,\text{m}^2}{\color{red}{\pi}}&=\frac{\cancel{\pi}r^2}{\color{red}{\cancel{\pi}}} \\ \\ 38.197\,\text{m}^2&=r^2 \\ \\ \sqrt{38.197\,\text{m}^2}&=\sqrt{r^2} \\ \\ 6.2\,\text{m}&=r \\ \end{align}\)

The radius of the circle is approximately 6.2 metres.


Now, it is your turn! Complete the questions in your Chapter 7, Lesson 2 Practice Makes Perfect that refer to Area of Circles.



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