Area of a Circle

Computer

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

images/circle-dia-circ.js

How to Summate the Area

The surface area of a circle is:

π (Pi) times the Radius squared: A = π r2

or, when you know the Diameter: A = (π/4) × D2

or, when you know the Circumference: A = C2 / 4π

Case: What is the area of a circle with radius of 3 chiliad ?

circle radius 3

Radius = r = 3

Area = π r2

= π × 32

= 3.14159... × (three × iii)

= 28.27 yard2 (to 2 decimal places)

How to Call back?

circle area pi r-squared (but pies are round!)
To help you lot remember think "Pie Are Squared"
(even though pies are usually round)

Comparing a Circle to a Square

Information technology is interesting to compare the surface area of a circle to a square:

circle area is about 80% of square

A circle has about 80% of the area of a similar-width foursquare.
The bodily value is (π/4) = 0.785398... = 78.5398...%

Why? Because the Square'southward Area is w2
and the Circle's Area is (π/four) × wii

Example: Compare a square to a circle of width 3 m

Square'due south Area = westii = 32 = ix m2

Estimate of Circle'south Expanse = lxxx% of Square's Expanse = 80% of nine = 7.ii mtwo

Circle'due south True Area = (π/4) × Dii = (π/four) × iii2 = 7.07 thousandtwo (to ii decimals)

The estimate of 7.2 thousand2 is not far off vii.07 yardtwo

A "Real World" Instance

Instance: Max is edifice a business firm. The first step is to drill holes and fill them with concrete.

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

circle auger

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

The bore is 0.4m, and then the Area is:

circle area example

A = (π/4) × D2

A = (iii.14159.../4) × 0.4ii

A = 0.7854... × 0.16

A = 0.126 1000two (to iii decimals)

And the holes are 1 m deep, so:

Book = 0.126 m2 × i thousand = 0.126 g3

And so Max should social club 0.126 cubic meters of concrete to make full each hole.

Note: Max could have estimated the expanse by:

  • 1. Calculating a square hole: 0.four × 0.4 = 0.sixteen m2
  • ii. Taking 80% of that (estimates a circle): lxxx% × 0.sixteen thouii = 0.128 thousand2
  • three. And the volume of a one thou deep pigsty is: 0.128 chiliadthree

And something interesting for you lot:

See Circle Area by Lines