how to find a radius of a circle

Radius Of A Circle

The radius of a circle is a line segment with one stop at the center of the circumvolve, and the other end on the circle itself. The radius is identified with a lower-case, italic $r$.

Table Of Contents

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1. Radius Of A Circumvolve
2. Radius Formula
3. Observe The Radius
   • Radius From Circumference
   • Radius From Area
   • Radius From Diameter
4. Radius Examples

Radius Of A Circle Formula

The formula y'all use depends on what is known about the circle. Below are 3 different formulas you can employ to detect the radius, $r$, of a circle.

Radius Formulas

If given...	And so...
Circumference (C)	$r=\frac{C}{\mathrm{two}\pi }$
Area (A)	$r=\sqrt{\frac{A}{\pi }}$
Diameter (d)	$r=\frac{d}{2}$

The relationship between radius and diameter is an important one to know when learning to how to calculate the radius.

Since the radius is a line segment from the center to the circle, and the bore, $d$, is a line segment from on side of a circle through the center of a circle and out to the other side of the circle, information technology follows that a radius is $\frac{1}{2}$ a diameter.

How To Find The Radius Of A Circle

To find the radius of a circumvolve, plug the given information into the right formula. You can find the radius of whatsoever circle if y'all are given the circumference, area, or diameter.

How To Discover Radius From Circumference

No matter the size of the circle, the relationship of the radius to the circumference, $C$, is a abiding, giving us the formula to find radius from circumference:

You can also summate the circumference of a circle with a given radius by using algebra to isolate the $C$ in our formula.

The radius to circumference formula is: $C=\mathrm{ii}\pi r$

Radius Of Circle From Expanse

You can use the area to observe the radius and the radius to find the area of a circle. The expanse of a circumvolve is the infinite information technology occupies, measured in square units.

Given the area, $A$, of a circle, its radius is the foursquare root of the area divided by pi:

The formula for radius to area is: $A=\pi r^{\mathrm{ii}}$

How To Discover Radius From Bore

If you know the diameter of a circle, you can find its radius by dividing the diameter by $\mathrm{two}$:

This is the simplest formula you can use to get the radius.

If you need to get from radius to diameter, multiply radius times $2$: $d=2r$

Radius Of A Circle Example

1. A circumvolve has a diameter of $6i\mathrm{northward}ches$. What is its radius?
2. A circle has a radius of $98feet$. What is its bore?
3. A circle with a circumference of $365\mathrm{yard}eters$ will accept a radius of how many meters?
4. A circle with a radius of $11i\mathrm{due\; north}ch\mathrm{eastward}s$ volition take a circumference of how many inches?
5. With a radius of $41\mathrm{chiliad}m$, a circle will accept an surface area equal to, what?
6. What is the radius of the following circle?

We don't like to talk in circles, but brand sure you lot piece of work these out before checking the answers below!

1. The radius of a $6i\mathrm{due\; north}ch$ circumvolve is $\mathrm{three}i\mathrm{due\; north}ch\mathrm{due\; east}s$.
2. A circle has a radius of $98feet$, so its diameter must be $196feet$.
3. A circumvolve with a circumference of $365\mathrm{thousand}\mathrm{eastward}ters$ will accept a radius of $58.4\mathrm{chiliad}\mathrm{east}ters$.
4. A circle with a radius of $\mathrm{xi}inche\mathrm{due\; south}$ will have a circumference of $69.12inches$.
5. With a radius of $41\mathrm{yard}illimeters$, a circumvolve will have an surface area of roughly $\mathrm{5,281.02}squaremil\mathrm{50}i\mathrm{one\; thousand}\mathrm{east}ters$ or $\mathrm{one\; thousand}{m}^2$.
6. The radius of the circle in the image above is $75m$.

Next Lesson:

Area Of A Circle

Source: https://tutors.com/math-tutors/geometry-help/how-to-find-the-radius-of-a-circle

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