Expanse of a Circle

Calculator

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

images/circumvolve-dia-circ.js

How to Calculate the Area

The area of a circle is:

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

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

or, when you lot know the Circumference: A = C2 / ivπ

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

circle radius 3

Radius = r = iii

Area = π r2

= π × iiitwo

= 3.14159... × (3 × 3)

= 28.27 mtwo (to two decimal places)

How to Call back?

circle area pi r-squared (but pies are round!)
To assist you lot recall call back "Pie Are Squared"
(even though pies are unremarkably round)

Comparing a Circle to a Foursquare

It is interesting to compare the surface area of a circumvolve to a square:

circle area is about 80% of square

A circle has about 80% of the expanse of a like-width square.
The actual value is (π/four) = 0.785398... = 78.5398...%

Why? Considering the Square's Expanse is west2
and the Circle's Area is (π/four) × w2

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

Square'south Area = w2 = 3ii = 9 m2

Estimate of Circle's Surface area = 80% of Foursquare's Area = 80% of nine = 7.ii m2

Circle's Truthful Area = (π/4) × Dtwo = (π/4) × iiiii = 7.07 chiliad2 (to two decimals)

The approximate of 7.2 gii is not far off 7.07 m2

A "Real World" Case

Case: Max is building a business firm. The first step is to drill holes and make full them with concrete.

The holes are 0.4 m wide and 1 m 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 diameter is 0.4m, and so the Area is:

circle area example

A = (π/4) × Dtwo

A = (iii.14159.../four) × 0.42

A = 0.7854... × 0.16

A = 0.126 g2 (to 3 decimals)

And the holes are one g deep, and so:

Volume = 0.126 one thousand2 × 1 m = 0.126 one thousandiii

And so Max should order 0.126 cubic meters of physical to fill each pigsty.

Note: Max could have estimated the area past:

  • 1. Calculating a square hole: 0.4 × 0.iv = 0.16 g2
  • 2. Taking 80% of that (estimates a circle): 80% × 0.16 m2 = 0.128 m2
  • 3. And the volume of a i m deep hole is: 0.128 one thousand3

And something interesting for you:

Come across Circle Expanse by Lines