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. Show TL;DR (Too Long; Didn't Read)The area of a circle is the amount of space the circle covers. The formula for calculating the area of a circle is A = πr2 where pi (π) equals 3.14 and the radius (r) is half the diameter. 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. Once you have the diameter (d) of the circle, you can find the radius (r) using the equation d=2r. The radius of a circle is the distance from the center of the circle to any point on the edge of the circle. The radius is also half of the diameter. If your diameter is a simple number, you can likely calculate the radius in your head. If not, rearrange the equation to find for r r = \frac{d}{2} and solve. You are now ready to use the equation for area: A = πr^2 Pi (π) is a non-algebraic number that represents the ratio of the distance around the circle (circumference) to its diameter, usually estimated as 3.14. To solve for area, square the radius (radius times radius) then multiply by 3.14. Since area is a measure of two dimensions, you always report area in square units like square inches (in2) or square feet (ft2). 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. CalculatorEnter the radius, diameter, circumference or area of a Circle to find the other three. The calculations are done "live": images/circle-dia-circ.js How to Calculate the AreaThe area of a circle is: π (Pi) times the Radius squared:A = π r2 or, when you know the Diameter:A = (π/4) × D2 or, when you know the Circumference:A = C2 / 4π Example: What is the area of a circle with radius of 3 m ?Radius = r = 3 Area= π r2 = π × 32 = 3.14159... × (3 × 3) = 28.27 m2 (to 2 decimal places) How to Remember? To help you remember think "Pie Are Squared" (even though pies are usually round) Comparing a Circle to a SquareIt is interesting to compare the area of a circle to a square: A circle has about 80% of the area of a similar-width square. Why? Because the Square's Area is w2 Example: Compare a square to a circle of width 3 mSquare's Area = w2 = 32 = 9 m2 Estimate of Circle's Area = 80% of Square's Area = 80% of 9 = 7.2 m2 Circle's True Area = (π/4) × D2 = (π/4) × 32 = 7.07 m2 (to 2 decimals) The estimate of 7.2 m2 is not far off 7.07 m2 A "Real World" ExampleExample: Max is building a house. The first step is to drill holes and fill them with concrete.The holes are 0.4 m wide and 1 m deep, how much concrete should Max order for each hole? The holes are circular (in cross section) because they are drilled out using an auger. The diameter is 0.4m, so the Area is: A = (π/4) × D2 A = (3.14159.../4) × 0.42 A = 0.7854... × 0.16 A = 0.126 m2 (to 3 decimals) And the holes are 1 m deep, so: Volume = 0.126 m2 × 1 m = 0.126 m3 So Max should order 0.126 cubic meters of concrete to fill each hole. Note: Max could have estimated the area by:
And something interesting for you: See Circle Area by Lines |
How to determine the area of a circle
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