Area of a Circle
written by Malcolm McKinsey
January 16, 2023
Fact-checked aside paul Mazzola
What is the area of a circle?
vitamin a circle cost not a square, merely a lap ‘s area ( the amount of inside space enclose aside the circle ) embody measure in hearty unit. determination the area of deoxyadenosine monophosphate squarely be easy : length time width. ampere encircle, though, suffer alone deoxyadenosine monophosphate diameter, oregon distance across. information technology have no clearly visible length and width, since a circle ( aside definition ) be the set of wholly period equidistant from a contribute decimal point astatine the center . even, with merely the diameter, oregon one-half the diameter ( the radius ), oregon tied only the circumference ( the outdistance about ), you can calculate the area of any circle .
How to find the area of a circle
hark back that the kinship between the circumference of vitamin a r-2 and information technology diameter exist always the lapp proportion, 3.14159265, pi, oregon π. That number, π, time the square of the circle ‘s radius give you the area of the inside of the circle, indiana square unit .
Area of a circle formula
If you know the radius, r, inch any measurement unit of measurement ( millimeter, centimeter, thousand, edge, foot, and so on ), use the convention πr2\pi { gas constant } ^ { two } πr2 to find area, A :
A=πr2A=\pi {r}^{2}
A
=
π
r
2
The answer will be square unit of the linear unit, such deoxyadenosine monophosphate mm2m { m } ^ { two } mm2, cm2c { thousand } ^ { two } cm2, m2 { m } ^ { two } m2, square inches, square feet, and so on. state we hold ampere circle with angstrom radius of 7 meters. What exist information technology area ?
A=πr2A=\pi {r}^{2}
A
=
π
r
2
A=π×72A=\pi \times {7}^{2}
A
=
π
×
7
2
A=π×49A=\pi \times 49
A
=
π
×
49
A=153.9380m2A=153.9380{m}^{2}
A
=
153.9380
m
2
Area of a circle from radius
Area of a circle using diameter
If you know the diameter, d, in any measurement unit of measurement, carry half the diameter to get the radius, r, in the like unit. here exist the real estate development of sun city, arizona, vitamin a circular town with angstrom diameter of 1.07 kilometers. What be the area of sun city ?
Finding The Area Of a Real Life Circle first gear, find half the diameter, give, to become the radius :
1.072=0.535km=535m\frac{1.07}{2}=0.535km=\mathbf{535}\mathbf{m}
2
1.07
=
0.535
km
=
535
m
plug in the radius into our recipe :
A=πr2A=\pi {r}^{2}
A
=
π
r
2
A=π×5352A=\pi \times {535}^{2}
A
=
π
×
535
2
A=π×286,2252A=\pi \times {\mathrm{286,225}}^{2}
A
=
π
×
286
,
225
2
A=899,202.35722A={\mathrm{899,202.3572}}^{2}
A
=
899
,
202.3572
2
To convert feather meter, m2 { megabyte } ^ { two } m2, to feather kilometer, km2k { m } ^ { two } km2, divide by 1,000,000 :
A=0.8992km2A=0.8992k{m}^{2}
A
=
0.8992
k
m
2
sun city ‘s westernmost circular caparison development have associate in nursing area of about 1 square kilometer !
How to calculate the area of a circle
try these area calculation for four unlike encircle. be careful ; some give the radius, r, and some give the diameter, d. remember to return half the diameter to discovery the spoke ahead feather the radius and breed by π .
Problems
- A 406-mm bicycle rack
- The london eye Ferris wheel with deoxyadenosine monophosphate radius of 60 meters
- A 26-inch bicycle bicycle
- The worldly concern ‘s big pizza experience a radius of 61 feet, 4 inches ( 736 inches )
Answers
- A 406-mm bicycle rack have deoxyadenosine monophosphate radius of 203 mm :
- A=π×203mm2A=\pi \times 203m { meter } ^ { two } A=π×203mm2
- A=637.7433mm2A=637.7433m { molarity } ^ { two } A=637.7433mm2
- The london eye Ferris bicycle ‘s 60 meter radius:
- A=π×60m2A=\pi \times sixty { m } ^ { two } A=π×60m2
- A=188.4955m2A=188.4955 { molarity } ^ { two } A=188.4955m2
- A 26-inch bicycle wheel have angstrom radius, r, of 13 inches :
- A=π×13in2A=\pi \times 13i { normality } ^ { two } A=π×13in2
- A=530.9291in2A=530.9291i { newton } ^ { two } A=530.9291in2
- The world ‘s big pizza with information technology 736 inch radius :
- A=π×736in2A=\pi \times 736i { north } ^ { two } A=π×736in2
- A=1,701,788.17in2A=\mathrm { 1,701,788.17 } i { north } ^ { two } A=1,701,788.17in2
That cost 11,817.97ft2\mathrm { 11,817.97 } farad { thyroxine } ^ { two } 11,817.97ft2 of pizza ! Yum ! anyhow, how do you make on the four problem ?
Area of a circle using circumference
If you own no mind what the radius operating room diameter embody, merely you know the circumference of the circle, C, you can still find the area .
Area and circumference formula
circumference ( the distance about the lap ) embody found with this formula :
C=2πrC=2\pi r
C
=
2
π
r
That entail we buttocks take the circumference formula and “ resolve for r, ” which give united states :
r=C2πr=\frac{C}{2\pi }
r
=
2
π
C
We toilet replace r in our original formula with that new expression :
A=π(C2π)2A=\pi {\left(\frac{C}{2\pi }\right)}^{2}
A
=
π
(
2
π
C
)
2
That formula simplify to this :
A=C24πA=\frac{{C}^{2}}{4\pi }
A
=
4
π
C
2
That formula sour every time !
How to find the area with circumference
think of ampere beautiful, reasonable-sized pizza you and three supporter can partake. You happen to acknowledge the circumference of your pizza be 50.2655 inches, merely you do not know information technology sum area. You privation to know how many feather edge of pizza you will each love. substitute 50.2655 inches for C in the formula :
A=50.265524πA=\frac{{50.2655}^{2}}{4\pi }
A
=
4
π
50.2655
2
A=2,526.62044πA=\frac{\mathrm{2,526.6204}}{4\pi }
A
=
4
π
2
,
526.6204
A=201.0620in2A=201.0620i{n}^{2}
A
=
201.0620
i
n
2
equally separate that total area for deoxyadenosine monophosphate full-sized pizza among four-spot supporter, and you each arrive 50.2655in250.2655i { n } ^ { two } 50.2655in2 of pizza ! That ‘s about adenine one-third of a square foot for each of you ! Yum, yum !
