# Area of a Circle

## Calculator

Enter the **radius, diameter, circumference** or **area** of a Circle to find the other three. The calculations are done "live":

## How to Calculate the Area

The area of a circle is:

^{2}

^{2}/ 4π

### Example: What is the area of a circle with radius of 3 m ?

Radius = r = 3

^{2}

^{2}

**28.27 m**(to 2 decimal places)

^{2}## How to Remember?

To help you remember think "Pie Are Squared"

(even though pies are usually *round*)

## Comparing a Circle to a Square

It is interesting to compare the area of a circle to a square:

A circle has **about 80%** of the area of a similar-width square.

The actual value is (π/4) = 0.785398... = **78.5398...%**

Why? Because the Square's Area is **w ^{2}**

and the Circle's Area is

**(π/4)**

**× w**

^{2}### Example: Compare a square to a circle of width 3 m

Square's Area = w^{2} = 3^{2 }= **9 m ^{2}**

Estimate of Circle's Area = 80% of Square's Area = 80% of 9 = **7.2 m ^{2}**

Circle's True Area = (π/4) × D^{2} = (π/4) × 3^{2 }= **7.07 m ^{2}** (to 2 decimals)

The estimate of **7.2 m ^{2}** is not far off

**7.07 m**

^{2}## A "Real World" Example

### Example: Max is building a house. The first step is to drill holes and fill them with concrete.

The holes are **0.4 m wide** and **1 m deep**, how much concrete should Max order for each hole?

The holes are circular (in cross section) because they are drilled out using an auger.

The diameter is 0.4m, so the Area is:

A = (π/4) × D^{2}

A = (3.14159.../4) × 0.4^{2}

A = 0.7854... × 0.16

A = **0.126 m ^{2}** (to 3 decimals)

And the holes are 1 m deep, so:

Volume = 0.126 m^{2} × 1 m = **0.126 m ^{3}**

So Max should order 0.126 cubic meters of concrete to fill each hole.

Note: Max could have **estimated** the area by:

- 1. Calculating a square hole: 0.4 × 0.4 =
**0.16 m**^{2} - 2. Taking 80% of that (estimates a circle): 80% × 0.16 m
^{2}=**0.128 m**^{2} - 3. And the volume of a 1 m deep hole is:
**0.128 m**^{3}