# Area of circle

In the last lesson, we learned that the formula for circumference of a circle is:. This relationship is expressed in the following formula:. The area of a circle is the number of square units inside that circle.

### Understanding the Square footage:

If each square in the circle to the left has an area of 1 cm 2you could count the total number of squares to get the area of this circle. Thus, if there were a total of Let's look at some examples involving the area of a circle. What is the area of the circle? What is the radius of the circle? We can also find the radius and diameter of a circle given its area. The formulas for the diameter and area of a circle are listed below:. Directions: Read each question below.

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## Calculate the Area of a Circle

The radius of a circle is 9 centimeters. The diameter of a circle is 12 inches. The radius of a circular rug is 4 feet. The area of a coin is 3. The diameter of a bicycle wheel is 20 inches. What is the area of the wheel?

Geometry and the Circle. Circumference of a Circle. Area of a Circle. Practice Exercises. Challenge Exercises. Circle Solver. Circumference and String. Geometry and a Shoebox. Geometry Worksheet Generator. Pre-Made Worksheets.One method of deriving this formula, which originated with Archimedesinvolves viewing the circle as the limit of a sequence of regular polygons. The area of a regular polygon is half its perimeter multiplied by the distance from its center to its sidesand the corresponding formula that the area is half the perimeter times the radius, i.

Although often referred to as the area of a circle in informal contexts, strictly speaking the term disk refers to the interior of the circle, while circle is reserved for the boundary only, which is a curve and covers no area itself. Therefore, the area of a disk is the more precise phrase for the area enclosed by a circle. Modern mathematics can obtain the area using the methods of integral calculus or its more sophisticated offspring, real analysis. However the area of a disk was studied by the Ancient Greeks. Eudoxus of Cnidus in the fifth century B. Prior to Archimedes, Hippocrates of Chios was the first to show that the area of a disk is proportional to the square of its diameter, as part of his quadrature of the lune of Hippocrates but did not identify the constant of proportionality. The most famous of these is Archimedes' method of exhaustionone of the earliest uses of the mathematical concept of a limitas well as the origin of Archimedes' axiom which remains part of the standard analytical treatment of the real number system.

The original proof of Archimedes is not rigorous by modern standards, because it assumes that we can compare the length of arc of a circle to the length of a secant and a tangent line, and similar statements about the area, as geometrically evident. The area of a regular polygon is half its perimeter times the apothem.

As the number of sides of the regular polygon increases, the polygon tends to a circle, and the apothem tends to the radius. This suggests that the area of a disk is half the circumference of its bounding circle times the radius. Following Archimedes' argument in The Measurement of a Circle c. If the area of the circle is not equal to that of the triangle, then it must be either greater or less.

We eliminate each of these by contradiction, leaving equality as the only possibility. We use regular polygons in the same way.

Let E denote the excess amount. Inscribe a square in the circle, so that its four corners lie on the circle. Between the square and the circle are four segments. If the total area of those gaps, G 4is greater than Esplit each arc in half. This makes the inscribed square into an inscribed octagon, and produces eight segments with a smaller total gap, G 8. Continue splitting until the total gap area, G nis less than E.

But this forces a contradiction, as follows. Draw a perpendicular from the center to the midpoint of a side of the polygon; its length, his less than the circle radius. Also, let each side of the polygon have length s ; then the sum of the sides, nsis less than the circle circumference.This generator makes worksheets for calculating the radius, diameter, circumference, or area of a circle, when one of those is given either radius, diameter, circumference, or area is given.

They can be made in PDF or html formats. Options are numerous: you can choose metric or customary units or both, you can include or not include simple circle images in the problems, or randomly let some problems have a circle image and some not.

You can also choose either 3. Please change the different options to see what their effect is. After you have generated a worksheet, you can just refresh the page from your browser window or hit F5 to get another worksheet with different problems but using the same options. All worksheets come with an answer key. You can print the worksheet directly from your browser, or save it on disk using the "Save as" command of your browser.

### Area of a Circle Calculator

If the problems on the worksheet don't fit the page or there is not enough working space, choose a smaller font, less cellpadding, or fewer columns of problems. Key to Geometry workbooks introduce students to a wide range of geometric discoveries as they do step-by-step constructions.

Using only a pencil, compass, and straightedge, students begin by drawing lines, bisecting angles, and reproducing segments. Later they do sophisticated constructions involving over a dozen steps-and are prompted to form their own generalizations. When they finish, students will have been introduced to geometric terms and will be ready to tackle formal proofs. Circle Worksheets. Do not use circle images in any problems. Use circle images in some problems randomly.

Choose problem types. Tick at least one box. The radius is given. Calculate the diameter of the circle. The circumference is given. The area is given.

The diameter is given. Calculate the radius of the circle.If you know the radius of the circle and the height of the segment, you can find the segment area from the formula below.

The result will vary from zero when the height is zero, to the full area of the circle when the height is equal to the diameter. If you know the central angle of the segment the angle subtended by the segment at the center of the circle you can use the method Area of a circular segment given the central angle. This calculation is useful as part of the calculation of the volume of liquid in a partially-filled cylindrical tank. For more on this see Volume of a horizontal cylindrical segment. Use the calculator below to calculate the segment area given the radius and height of the segment, using the formula described above.

Home Contact About Subject Index. Definition: The number of square units it takes to fill a segment of a circle. Try this Drag one of the orange dot that defines an endpoint of the segment. Adjust the segment height.

Note the number of square units it takes to fill it and the calculation. Calculate Clear.Area of a circle is simply, number of square units fit into a circle. Our circle area calculator, requires diameter OR radius of a circle to calculate area of a given circle. Are you looking to calculate circumference of a circle? Circumference Calculator.

Trapezoid Calculator Triangle Calculator Gravel Calculator Free calculator widget You can put this calculator widget on your website, web page or blog. Remember, the input can only be in feet ftinches inyards ydcentimetres cmmillimetres mm and metres m but never a combination of two different units!

To understand how to calculate square footage we must first begin with the definition of area. An area is the size of a two-dimensional surface. The area of a circle is the space contained within its circumference outer perimeter. To find out the area of a circle, we need to know its diameter which is the length of its widest part. The diameter should be measured in feet ft for square footage calculations and if needed, converted to inches inyards ydcentimetres cmmillimetres mm and metres m.

Our Square Footage Calculator helps you calculate the area required for making circular landscaping designs, carpeting, wall decals, centre moulding on a ceiling and floor tiling. Technology has advanced and with that, there have been many calculators which help users precisely measure things even from the comfort of their laptop or mobile phone.

Our area of circl calculator lets you easily find the area, circumference, radius or specific diameter of any circle. With any of these variables A, C, r or d of a circle, you can precisely measure the other three unknowns. You can use this formula in many real world examples such as when building a house, drilling, filling holes with concrete etc.

Essentially, the formula gives you accurate details on how much material you need or how big the surface you will drill into needs to be. However, you should also be aware that the area of a circle calculator demands other things which you need to know before measuring. Circles are complex shapes. Perhaps, their main variable is the radius — which is measured from the center of the circle to any of its sides.

Essentially, the diameter is twice the radius — or any line that goes from one side of the circle to the other while crossing its center. The circumference of a circle, however, is not that commonly understood by many.

Essentially, this variable can be defined as the distance around the circle or the entire length of the circuit along the circle. Used since ancient geometrics, all of these variables let you precisely calculate anything related to a circle. However, instead of doing things manually, now you can use our area of a circle calculator and make use of the ready circle formula. Whether you are in class solving a math test or need an accurate calculation about the area of a circle for a project that you are building, the formula for area of a circle is simple — but not that simple when you are left with a pen and paper.

All you need is another variable to get the other three and solve the problem immediately. You need to know the diameter of the circle in either feet ftinches inyards ydcentimetres cmmillimetres mm or metres m. You can calculate the area of the circle border in square feet, in square inches, square yards, square centimetres, square millimetres and square meters.

Yes, our tool is that awesome.A circle is one of the most widely recognizable geometric shapes, but exploring the mathematical concepts of diameter and area can sometimes feel tricky. Whether you are measuring the size of round rug you need to purchase or determining the space you need to construct a round garden or patio, knowing how to calculate the area of a circle from its diameter is a valuable skill. The area of a circle is the amount of space the circle covers. The first step for calculating the area of a circle from its diameter is to find that diameter.

While math problems often list this value, in the real world, you must find the diameter yourself. The diameter is the length of a line that begins at the edge of the circle, passes through the center of the circle, and ends at the opposite edge of the circle. To measure, you will need a ruler for small circles or a tape measure for large circles.

The radius of a circle is the distance from the center of the circle to any point on the edge of the circle.

Circles: Area, Circumference, Radius & Diameter Explained!

The radius is also half of the diameter. If your diameter is a simple number, you can likely calculate the radius in your head. To solve for area, square the radius radius times radius then multiply by 3. Since area is a measure of two dimensions, you always report area in square units like square inches in 2 or square feet ft 2.

This is especially important when calculating the area of a circle for an assignment since an answer without correctly reported units is likely incorrect or incomplete. Any time you need to determine the space inside a circle or the amount of space a circle covers, you can use the equation for the area of a circle. Especially for real world applications of this skill, measuring diameter is often the simplest way to start. Melissa Mayer is an eclectic science writer with experience in the fields of molecular biology, proteomics, genomics, microbiology, biobanking and food science.

She has also served as interim associate editor for a glossy trade magazine read by pathologists, Clinical Lab Products, and wrote a non-fiction YA book Coping with Date Rape and Acquaintance Rape. She has two books forthcoming covering the neuroscience of mental health. About the Author. Copyright Leaf Group Ltd.Area of a circle Calculator. Calculates the area and circumference of a circle given the radius or diameter. Customer Voice. Area of a circle.

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The hyperlink to [Area of a circle] Area of a circle Calculator. Related Calculator. Area of an equilateral triangle Area of a triangle given base and height Area of a triangle given sides and angle Area of a triangle Heron's formula Area of a triangle given base and angles Area of a square Area of a rectangle Area of a trapezoid Area of a rhombus Area of a parallelogram given base and height Area of a parallelogram given sides and angle Area of a cyclic quadrilateral Area of a quadrilateral Area of a regular polygon Side of polygon given area Area of a circle Radius of circle given area Area of a circular sector Area of an arch given angle Area of an arch given height and radius Area of an arch given height and chord Area of an ellipse Area of an elliptical sector Area of an elliptical arch Area of a parabolic arch Area of a hyperbolic sector Area of a hyperbolic arch Google maps area.

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