how to find the area of a circle with the radius
Radius
Radius is defined as a line segment joining the heart to the boundary of a circle or a sphere. The length of the radius remains the same from the center to whatever bespeak on the circumference of the circle or sphere. It is one-half of the length of the diameter. Let us learn more about radius in this commodity.
| ane. | What is Radius? |
| 2. | Radius Formulas |
| iii. | Radius of Circle |
| 4. | How to Notice the Radius of a Circle? |
| 5. | Radius of a Circle Equation |
| 6. | Radius of a Sphere |
| 7. | FAQs on Radius |
What is Radius?
In geometry, the radius is defined as a line segment joining the heart of the circumvolve or a sphere to its circumference or purlieus. It is an of import function of circles and spheres which is generally abbreviated as 'r'. The plural of radius is "radii" which is used when nosotros talk virtually more than one radius at a time. The largest line segment in a circle or sphere joining any points lying on the opposite side of the eye is the bore, and the length of the radius is half of the length of the diameter. It tin be expressed as d/2, where 'd' is the diameter of the circle or sphere. Look at the prototype of a circle given below showing the relationship between radius and diameter.
Now, let the states learn the formulas of radius that will assist you to calculate its length with the given information.
Radius Formulas
The radius of a circle and sphere tin be calculated using some specific formulas that yous are going to learn in this section. Here, nosotros will talk virtually radius formulas for a circle. The radius of a sphere formula is discussed in the section beneath.
Radius Formula from Bore: The diameter is a direct line passing through the heart and joining a point from one end to a point on the other terminate of the circumvolve. The diameter is twice the length of the radius. Mathematically, it is written as Bore = 2 × radius. It is also the longest chord of a circle. When the diameter of a circle is given, and then the radius formula is expressed as:
Radius = Diameter/ii or D/ii units
Radius Formula from Circumference: The perimeter of a circle is called its circumference. Information technology is the purlieus of a circle and can be expressed by the formula: C = 2πr units. Here, C is the circumference, r is the radius of the circle, and π is the constant which is equal to 3.14159. The radius is the ratio of circumference to 2π. The radius formula using the circumference of a circle is expressed equally:
Radius = Circumference/2π or C/2π units
Radius Formula with Surface area: The area of a circle is the space occupied by the circle. The human relationship between the radius and area is given past the formula, Expanse of the circumvolve = πrii square units. Here, r is the radius and π is the constant which is equal to iii.14159. The radius formula using the area of a circumvolve is expressed every bit:
Radius = √(Expanse/π) units
Radius of Circle
Radius is one of the important parts of a circle. It is the altitude between the middle of the circumvolve to any point on its boundary. In other words, when we connect the center of a circle to whatsoever point on its circumference using a straight line, that line segment is the radius of that circle. A circle can have more than than one radius because there are infinite points on its circumference. This means that a circle has an infinite number of radii and all the radii of the circumvolve are equidistant from the center of the circle. The size of the circle changes when the length of the radius varies.
In the figure given below, the points A, B, M, N, P, Q, 10, and Y lie on the boundary of the circle. Observe that these points are equidistant from the center O. Then, all the line segments OA, OB, OM, ON, OY, OX, OP, and OQ are termed as the radii of the circle. Observe that OA = OB = OM = ON = OP = OQ = OX = OY.
How to Notice the Radius of a Circle?
The radius of a circle can exist establish using the three bones radius formulas i.eastward., when the diameter, the area, or the circumference is known. Let us use these formulas to find the radius of a circle.
- When the diameter is known, the formula is Radius = Bore/ 2.
- When the circumference is known, the formula is Radius = Circumference/2π.
- When the area is known, the formula for the radius is Radius = ⎷(Area of the circle/π).
For example, if the diameter is given as 24 units, then the radius is 24/2 = 12 units. If the circumference of a circle is given every bit 44 units, and so its radius can be calculated as 44/2π. This implies, (44×7)/(two×22) = 7 units. And, if the area of a circle is given as 616 square units, then the radius is ⎷(616×7)/22 = ⎷28×vii = ⎷196 = 14 units.
Radius of Circle Equation
The radius of a circle equation on the cartesian plane with center (h, chiliad) is given equally (x − h)2 + (y − k)2 = r2. Here, (x, y) are the points on the circumference of the circle that is at a distance 'r' (radius) from the eye (h, k). When the eye of the circle is at origin (0,0), the equation of the circumvolve reduces to xtwo + ytwo = rii. Observe the diagram of a circle on the cartesian airplane shown below. Hither, the coordinates of the center are (0, b) and the radius of the circle is represented past 'r' joining the center to the point (x, y) on the circle. So, we just demand to substitute these values in the above equation to get the radius of the circle equation. The equation to find the radius of this circle is (10 − 0)two + (y − b)ii = rii ⇒ ten2 + (y − b)2 = r2.
Radius of a Sphere
A sphere is a 3D solid figure. The radius of the sphere is the segment from the center to any point on the boundary of the sphere. Information technology is a determining cistron while drawing a sphere as its size depends on its radius. Like a circle, there can exist space radii fatigued inside a sphere and all those radii volition exist equal in length. To calculate the sphere's volume and surface area, we demand to know its radius. And we can hands calculate the radius of the sphere from its volume and area formulas.
Radius of Sphere from Volume = 3⎷(3V)/4π units, where V represents the volume and the value of π is approximately 3.fourteen.
Radius of Sphere using Surface Area = ⎷(A/4π) units, where A represents the expanse.
Apply our free online radius of sphere estimator to summate the radius with the given volume, surface surface area, or diameter of a sphere.
☛ Related Articles
Check these interesting articles related to the radius and its formulas.
- Radius of Curvature Formula
- Segment of a Circumvolve
- Sector of a Circle
Radius of Circle Examples
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Practice Questions on Radius of Circle
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FAQs on Radius of Circle
What is the Radius of a Circle in Geometry?
The radius of a circumvolve is the length of the line segment from the center to a indicate on the circumference of the circle. It is generally abbreviated as 'r'. There tin can be infinite radii fatigued in a circumvolve and the length of all those radii volition be the same. It is half of the bore of the circumvolve.
How is Diameter Related to the Radius of the Circle?
The diameter of a circle is twice the radius, or, the radius is half the diameter. The relation betwixt radius and bore can be expressed in the formula: Diameter = two × radius. Use a complimentary online radius figurer to calculate the radius with the given diameter.
How to Notice the Radius of a Circle with the Circumference?
The circumference of a circle and radius are related to each other and their relation can be expressed as Circumference = 2πR, where R is the radius. Then, when the circumference is known, the formula used to summate the radius of a circle is Radius = Circumference / 2π.
What is the Radius of a Bend?
The radius of a curve or an arc is the radius of the circle of which it is a part. When the length of the chord defining the base (W) and the meridian measured at the midpoint of the arc's base (H) is given, the formula to find the radius is Radius = (H / two) + (Due west2 / 8H).
What is the Radius Formula?
The radius of a circumvolve can be calculated through various formulas. Discover the following formulas to calculate the radius:
- When the diameter is known, the formula is Radius = Diameter / ii.
- When the circumference is known, the formula for the radius is Circumference / 2π.
- When the area is known, the formula is Radius = ⎷(Expanse of the circle / π).
How to Calculate Radius of Circumvolve Using Calculator?
The length of the radius is equal to half the length of the bore that can be calculated using Cuemath'south online calculator by simply entering any given value amid, diameter, circumference, or expanse of a circumvolve.
How to Detect the Radius of a Circle with the Surface area?
If the expanse of a circumvolve is given, then the formula to find the radius is given as Radius = ⎷(A/π) units, where A is the given surface area.
Source: https://www.cuemath.com/geometry/radius/
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