How Do You Find the Diameter of a Circle if You Know Its Area
Related Pages
Geometry: Circles
Angles In A Circle
Conic Sections: Circles
We have as well added an Expanse of Circle calculator at the end of this page.
The following diagram gives the formula for the area of a circle. Scroll downward the page for more examples and solutions on how to use the formula and also a proof or the formula.
Formula for the Surface area of a Circumvolve
A circle is a airtight curve formed past a set of points on a aeroplane that are the aforementioned distance from its eye. The surface area of a circle is the region enclosed by the circle. The surface area of a circle is equals to pi (π) multiplied by its radius squared.
Pi (π) is the ratio of the circumference of a circumvolve to its diameter. Pi is always the same number for whatsoever circle. The value of π (pi) is approximately 3.14159265358979323846… but usually rounding to three.142 should be sufficient.
The surface area of a circle is given by the formula:
A = πr2 (see a mnemonic for this formula)
where A is the area and r is the radius.
Since the formula is only given in terms of radius, remember to alter from diameter to radius when necessary. The radius is equals to half the bore.
Expanse of a circle given the diameter or radius
Instance 1:
Find the area the circle with a diameter of 10 inches.
Solution:
| Pace 1: Write downward the formula: | A = πrii |
| Step two: Modify bore to radius: |  |
| Pace 3: Plug in the value: | A = π5ii = 25π |
Respond: The area of the circle is 25π ≈ 78.55 square inches.
Case two:
Detect the area the circle with a radius of 10 inches.
Solution:
| Stride 1: Write down the formula: | A = πrtwo |
| Pace two: Plug in the value: | A = π102 = 100π |
Answer: The area of the circle is 100π ≈ 314.ii foursquare inches.
See also:
Area of a Sector
Worksheet to calculate the area of circle
Worksheet to calculate circumference and area of circle when given bore or radius
How to use the formula A = πr2 to calculate the surface area of the circle given the radius?
Example:
Find the area of a circle with radius 4cm.
- Prove Video Lesson
How to employ the formula to calculate the area of the circle given the radius or the diameter?
Example:
- Find the area of a circle with radius 3cm.
- Find the area of a circle with diameter 20cm.
- Bear witness Video Lesson
Give-and-take Problems using area of circles
The following videos show how to solve word problems using the area of circles.
Instance:
There are ii circles such that the radius of the larger circle is 3 times the radius of the smaller circle.
(a) How many times the circumference of the larger circle is the circumference of the smaller circle?
(b) What is the ratio of the surface area of the larger circumvolve to the area of the smaller circle?
- Show Video Lesson
Area and Circumference Give-and-take Bug
Case 1: Janell wants to replace the glass in her mirrors. She can buy glass for $0.89 per foursquare inch. If the price includes tax, how much would she pay, to the nearest penny?
Example 2: The rectangle has a length of 21 inches and each circle is coinciding. What is the expanse of one circumvolve?
Example 3: A tire from Karen's machine is shown beneath. What is the closest distance traveled, in feet, after 3 full rotations of the tire?
- Show Video Lesson
Notice radius or bore of a circumvolve when given the expanse
From the formula A = πr2, we come across that we can find the radius of a circle past dividing its area by π and then become the positive square-root. The diameter is then twice the radius. This video shows how to find the radius or bore of a circle when given the area.
Examples:
The area of a circumvolve is 12.56 yd2. What is the circle's bore? (take π = 3.xiv)
- Show Video Lesson
Notice the circumference of a circle, given the area
Worksheet to calculate bug that involve the radius, bore, circumference and expanse of circle
Worksheet on word problems that involve circles 1
Worksheet on word problems that involve circles 2
To find the circumference of a circle when given the area, we get-go apply the surface area to discover the radius. And so, nosotros apply the radius to find the circumference of the circle.
How to observe the circumference of a circle given the area?
Instance:
The area of the circle is 12.56 cmii. What is the circumvolve's circumference?
- Show Video Lesson
How to calculate areas of circles and also composite shapes with circles or segments of circles?
The shape is made from four semicircles of diameter 8m and a square of side 8m. The radius of each circle is therefore 4m, and you have the equivalent of 2 whole circles. And so add on the expanse of the square.
- Show Video Lesson
Proof for the formula of a circle
The following diagram shows a visual proof for the formula of the expanse of a circle.
Graphical proof of the formula of a circumvolve
Information technology involves dividing the circle into many sectors and rearranging the sectors to form a rectangle. The base of the rectangle is shown to be πr and the top of the rectangle is r. The area of the rectangle is and so the product of πr and r. The expanse of the circle which is equal to area of the rectangle is so πr2.
- Show Video Lesson
Area of Circle Calculator
Enter the radius and this expanse of circle calculator will requite you lot the expanse. Use it to check your answers.
Attempt the free Mathway computer and trouble solver below to practice various math topics. Try the given examples, or blazon in your own problem and check your reply with the step-past-step explanations.
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