Surface area of a Circle

Computer

Enter the
radius, bore, circumference
or
surface area
of a Circle to observe 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
rtwo

or, when yous know the Diameter:
A = (π/four) × D2

or, when yous know the Circumference:
A = Cii
/ 4π

Example: What is the surface area of a circumvolve with radius of 3 thousand ?

Radius = r = 3


Area


=
π
r2



=
π
× 3two



= three.14159… × (3 × 3)



=
28.27 mtwo

(to two decimal places)

How to Retrieve?

circle area pi r-squared (but pies are round!)

To help y'all think think "Pie Are Squared"
(even though pies are normally
circular)

Comparing a Circumvolve to a Square

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

circle area is about 80% of square

A circle has
most 80%
of the area of a like-width square.
The actual value is (π/4) = 0.785398… =
78.5398…%

Why? Considering the Foursquare'south Surface area is
wtwo

and the Circle'south Surface surface area is
(π/iv)
× w2

Example: Compare a square to a circle of width three k

Foursquare'southward Area = due due westtwo
= three2
=
9 one g2

Judge of Circle's Surface area = eighty% of Square'due south Area = eighty% of nine =
7.2 10002

Circle'south True Surface area = (π/4) × Dtwo
= (π/4) × threetwo
=
7.07 yard2

(to 2 decimals)

The estimate of
seven.ii 1000two

is not far off
vii.07 mtwo

A "Real World" Instance

Example: Max is edifice a business firm. The first stride is to drill holes and make full them with physical.

The holes are
0.4 one thousand wide
and
one grand deep, how much concrete should Max social club for each pigsty?

circle auger

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

The diameter is 0.4m, so the Expanse is:

circle area example

A = (π/4) × D2

A = (iii.14159…/four) × 0.42

A = 0.7854… × 0.16

A =
0.126 yard2

(to three decimals)

And the holes are 1 m deep, then:

Volume = 0.126 mtwo
× 1 m =
0.126 chiliadiii

So Max should social society 0.126 cubic meters of concrete to fill up each hole.

Annotation: Max could accept
estimated
the area past:

  • i. Computing a square hole: 0.4
    × 0.4 =
    0.16 1 ktwo

  • two. Taking eighty% of that (estimates a circle):

    80% × 0.sixteen mii

    =
    0.128 mii
  • three. And the book of a i g deep hole is:

    0.128 mthree

And something interesting for you:

Come across Circle Area past Lines