AREA AND CIRCUMFERENCE OF A CIRCLE

AREA AND CIRCUMFERENCE OF A CIRCLE. In our previous article, we discussed the length of an arc of a circle and worked out some calculations on that topic. In this article, we will look at the area of a circle and the circumference of a circle. We will also consider how to find the radius of a circle given the area and the circumference of the circle.

THE CIRCUMFERENCE OF A CIRCLE

We use the term circumference as the distance around something round, oval, or rounded. The circumference is the perimeter of a circle. In other words, it is the length of the circle if it were to be opened up or stretched out to a line segment. In general, a perimeter is the curve length around any closed shape.

The formula for the circumference of a circle, C=2πr

Where C = circumference

π = the constant pi which has the value  is 3.142 or \frac{22}{7}.

r = radius of the circle

HOW TO CALCULATE THE CIRCUMFERENCE OF A CIRCLE

The circumference of a circle can be determined by using either the radius or the diameter. The circumference of a circle is written as:

Circumference =2r\times π or d\times π

Where π is the unit of measuring angles in radian, r is the radius and d is the diameter of the circle.

Note: The perimeter of a circle is the same as the circumference of the circle. So don’t get confused when you are asked to find the perimeter of a circle.

Let us now consider a few examples of how to calculate the circumference or perimeter of a circle.

Example 1: Find the circumference of a circle whose diameter is 6cm. {Take π = \frac{22}{7}}.

The diameter of the circle is 6cm, and π=\frac{22}{7}

Therefore, the Circumference of the circle =d\times π

∴ Circumference of the circle 6\times \frac{22}{7}=6\times 3.142=18.85cm

Example 2: Find the diameter of a circle whose circumference is 21.98m {Take π=\frac{22}{7}}.

If the circumference of the circle,  c=21.98m

Then Diameter, d=\frac{c}{\barwedge } =\frac{21.98}{\frac{22}{7}}=\frac{21.98}{3.142}=6.99m

You see! it’s easy!

Now, let’s move a step further to see how to calculate the area of a circle. Remember we promised to discuss these two terms – circumference and the area of a circle in this article.

Recommended: Circle-Perimeter, Area of a sector of a circle, Quadratic Equation, Logarithms of Numbers.

Watch Series of Mathematics Past Questions Solution Videos from the New Track Mathematics Video Past Questions Playlist. Click HERE to watch.

AREA OF A CIRCLE

The area of a cassettes disk (CD) is the more precise analogy to the area enclosed by a circle. The disk refers to the interior of the circle. With this comparison, we can define the area of a circle as the space or region enclosed within the circle.

The area enclosed by a circle of radius r is πr^{2}. π is the constant ratio of the perimeter of any circle to the diameter, and r is the radius of the circle.

The area of a circle with a radius, r is π \times r^{2} square unit. So, therefore, the area of a circle = πr^{2}.

The examples below explain how to find the area of a circle, given the radius or diameter of a circle .

Example 1: Find the area of a circle of radius 5cm. {Take π=\frac{22}{7}}

Given the parameters, r=5cm, π=\frac{22}{7}=3.142

Area=πr^{2}=\frac{22}{7}\times 5^{2}=\frac{22\times 25}{7}

\therefore Area=\frac{550}{7}=78.57cm^{2}

Let us consider another example. This time we are asked to look for the area of a circle, given the circumference of the circle.

Note: To find the area of a circle given the circumference, use this formula:

The area of a circle = \frac{C^{2}}{4\barwedge }

Where, C is the Circumference of the circle, and π is pie. 

Example 2: Find the area of a circle whose circumference is 24cm.

Given that the Circumference, C = 24cm and π = \frac{22}{7}

Area of the circle, A = \frac{C^{2}}{4\barwedge }

A=\frac{24^{2}}{4\times \frac{22}{7}}

A=\frac{576}{\frac{88}{7}}

A=576 ÷ \frac{88}{7}

A=576\times \frac{7}{88}

A=\frac{4032}{88}=45.8cm^{2}

You see the solution is very easy! What if you are asked to find the area of a circle given the diameter, D of the circle. In that instance, I want you to use this formula: Area of a circle, A=\frac{\barwedge D^{2}}{4}

Example 3: Find the area of a circle given that the diameter of the circle is 10cm.

Given the diameter, D = 10cm and π = \frac{22}{7}

Area of the circle, A=\frac{\barwedge D^{2}}{4}

A=\frac{\frac{22}{7}\times 10cm^{2}}{4}

A=\frac{\frac{22}{7}\times 100cm^{2}}{4}

A=\frac{\frac{2200}{7}}{4}=\frac{314.28}{4}

A=78.6cm^{2}

All the above examples show that finding the area of a circle can be very easy. Try solving similar questions from pool of questions that may be available to you.

Other topics you might want to learn is “Logarithm”. The use of Logarithm Table is an interesting topic. The video below will teach you with graphics how to use the Mathematical and formula table. Watch and learn!

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January 5, 2022
MATH ARTICLES

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