Area Of Circular Ring Formula

Table Of Contents

1. What Is The Expanse Of A Circle?
2. How To Find The Area Of A Circumvolve
• Area Of A Circumvolve Formula
• Area Of A Circle Using Bore
3. How to Calculate the Area of a Circumvolve
4. Area Of A Circumvolve Using Circumference
• Area and Circumference Formula
• How To Find Area With Circumference

What Is The Area Of A Circle?

A circle is not a foursquare, but a circle'south area (the amount of interior space enclosed by the circle) is measured in square units. Finding the expanse of a foursquare is easy: length times width.

A circle, though, has only a diameter, or distance across. It has no clearly visible length and width, since a circumvolve (by definition) is the set of all points equidistant from a given point at the center.

Yet, with just the bore, or one-half the diameter (the radius), or even only the circumference (the altitude around), you lot tin calculate the area of any circle.

How To Observe The Area Of A Circle

Recall that the human relationship betwixt the circumference of a circle and its diameter is e'er the same ratio, $3.14159265$, pi, or $\pi$. That number, $\pi$, times the square of the circle's radius gives you the expanse of the within of the circle, in square units.

Area Of A Circle Formula

If you know the radius, $r$, in whatever measurement units (mm, cm, yard, inches, feet, and then on), use the formula π r² to find surface area, $A$:

The respond will be square units of the linear units, such as $\mathrm{grand}{m}^{\mathrm{two}}$, $c{\mathrm{yard}}^2$, ${\mathrm{grand}}^{\mathrm{ii}}$, square inches, foursquare feet, and and so on.

Here is a circle with a radius of 7 meters. What is its area?

[insert drawing of fourteen-m-wide circle, with radius labeled 7 m]

$A=\pi ·r^{\mathrm{ii}}$

$A=\pi \times 7^2$

$A=\pi \times 49$

$\mathbf{A}\mathbf{=}\mathbf{153.9380}{\mathbf{m}}^{\mathbf{2}}$

Expanse Of A Circle Using Diameter

If you know the bore, $d$, in whatever measurement units, take half the diameter to get the radius, $r$, in the same units.

Here is the real estate development of Sunday City, Arizona, a circular town with a diameter of $1.07$ kilometers. What is the area of Sun City?

First, find half the diameter, given, to become the radius:

$\frac{1.07}{\mathrm{two}}=0.535mk=\mathbf{535}\mathbf{m}$

Plug in the radius into our formula:

$A=\pi ·r^{\mathrm{two}}$

$A=\pi \times {535}^2$

$A=\pi \times \mathrm{286,225}$

$A=\mathrm{899,202.3572}{m}^2$

To convert square meters, $k^{\mathrm{ii}}$, to square kilometers, $k{\mathrm{yard}}^2$, divide by $\mathrm{1,000,000}$:

$\mathbf{A}\mathbf{=}\mathbf{0.8992}{\mathbf{km}}^{\mathbf{2}}$

Sun City'south westernmost circular housing development has an area of nearly 1 square kilometer!

How to Calculate the Expanse of a Circle

Try these expanse calculations for four different circles. Be conscientious; some give the radius, $r$, and some give the diameter, $d$.

Remember to accept half the diameter to find the radius before squaring the radius and multiplying by $\pi$.

Bug

1. A 406-mm bicycle wheel
2. The London Centre Ferris wheel with a radius of 60 meters
3. A 26-inch wheel cycle
4. The world'south largest pizza had a radius of 61 feet, 4 inches (736 inches)

Do not peek at the answers until you do your calculations!

Answers

1. A 406-mm wheel bike has a radius, $r$, of 203 mm:

$A=\pi r^{\mathrm{two}}$

$A=\pi \times 203m{m}^2$

$A=637.7433\mathrm{chiliad}{\mathrm{thou}}^2$

2. The London Middle Ferris wheel'south 60-meter radius:

$A=\pi r^{\mathrm{two}}$

$A=\pi \times \mathrm{sixty}{\mathrm{thou}}^2$

$A=188.4955g^2$

3. A 26-inch bicycle wheel has a radius, $r$, of 13 inches:

$A=\pi r^2$

$A=\pi \times 13i{n}^2$

$A=530.9291i{\mathrm{north}}^2$

4. The world's largest pizza with its 736-inch radius:

$A=\pi r^{\mathrm{ii}}$

$A=\pi \times 736i{n}^2$

$A=\mathrm{1,701,788.17}i{n}^2$

That is $\mathrm{11,817.97}f{t}^{\mathrm{two}}$ of pizza! Yum! Anyhow, how did y'all do on the four issues?

Surface area Of A Circle Using Circumference

If you have no idea what the radius or diameter is, only you know the circumference of the circle, $C$, you can still notice the area.

Surface area and Circumference Formula

Circumference (the altitude effectually the circle) is found with this formula:

$C=2\pi r$

That ways we tin can have the circumference formula and "solve for $r$," which gives us:

$r=\frac{C}{\mathrm{ii}\pi }$

We tin supersede $r$ in our original formula with that new expression:

$A=\pi {\left(\frac{C}{2\pi }\right)}^2$

That expression simplifies to this:

That formula works every fourth dimension!

How To Find The Area With Circumference

Hither is a beautiful, reasonable-sized pizza you lot and three friends can share. You lot happen to know the circumference of your pizza is $50.2655$ inches, but yous practise not know its total surface area. You want to know how many square inches of pizza yous will each enjoy.

[insert cartoon drawing of typical 16-inch pizza but do non label bore]

Substitute $50.2655$ inches for $C$ in the formula:

$A=\frac{{\mathrm{fifty.2655}}^2}{4\pi }$

$A=\frac{\mathrm{two,526.6204}}{\mathrm{four}\pi }$

$\mathbf{A}\mathbf{=}\mathbf{201.0620}{\mathbf{in}}^{\mathbf{two}}$

Every bit divide that total area for a full-sized pizza among iv friends, and you each get $50.2655i{n}^2$ of pizza! That's about a 3rd of a foursquare foot for each of you! Yum, yum!

Next Lesson:

Area of a Sector of a Circle

Area Of Circular Ring Formula,

Source: https://tutors.com/math-tutors/geometry-help/area-of-a-circle

Posted by: hoagmusly1952.blogspot.com

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