Mark, a mathematics enthusiast, loves creating tutorials because that stumped students and those who need to brush increase on their math skills.

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In this article, ns will display you exactly how to discover the area of a circle and also express your answer in terms of pi (π). First, you'll should familiarize yourself with the formula because that calculating the area the a circle:


A = π * r²

Let's define our variables:

A: area that the circleπ: pi (a mathematical constant that is roughly equal come 3.141492 . . .)r: radius the the circle (the street from the circle's center allude to its edge)

Typically, to find the area of a circle, us would merely plug in the circle's radius for r and 3.141592 because that π. If so, our answer would certainly be a number.

How do You Get solution in regards to pi (π)?

To express your answer in terms of pi, simply refrain indigenous substituting pi's numerical worth for its price in the equation. That way, her answer will look choose where x is every little thing number you come increase with, and π is just a placeholder because that pi's worth (3.141582 . . .). Essentially, by expressing her answer in terms of pi, you room cutting one action out of your calculation. Let's take a look at part examples.


Example troubles With Processes and Solutions

In each of the following instance problems, we'll work through the process of recognize a circle's area in regards to pi using only its radius or diameter.

Example 1

Work out the area the a circle that has actually a radius of 7 m. Provide your price in regards to pi.

All you should do is substitute 7 for r in A = π * r²

A = π * r²

A = π * 7²

A = π * (7 * 7)

A = π * 49

A = 49π

So the last answer is 49π m2 (put the number prior to pi and also put your answer in regards to the appropriate units squared).

Example 2

Work the end the area of one that has a diameter the 22 cm. Give your price in regards to pi.


This time, the diameter (the street all the means across the circle, or double its radius) is given, so we'll should halve this to offer the radius. Due to the fact that the diameter is 22 cm, the radius is 11 cm, or half of that.

A = π * r²

A = π * 11²

A = π * (11 * 11)

A = π * 121

A = 121π

So the last answer is 121π cm² (put the number before pi and put her answer in terms of the relevant units squared).


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This one lawn has actually a radius the 13m, therefore our answer v be in meters squared.


Example 3

Work the end the area of the one lawn displayed in the picture above. Offer your price in regards to pi.

The radius of this lawn is 13 m, therefore we'll have to plug this value into the formula.

A = π * r²

A = π * 13²

A = π * (13 * 13)

A = π * 169

A = 169π

So the last answer is 169π m² (put the number before pi and also put her answer in regards to the relevant units squared).

This content is accurate and true to the ideal of the author’s knowledge and also is not meant to substitute for formal and also individualized advice native a qualified professional.


Questions & Answers

Question: deserve to you work out the perimeter that a semicircle with a radius of 3cm? offer your prize in regards to pi?

Answer: To occupational out the cirumference main point the diameter by pi.

The diameter is 6, and so 6 multiply by Pi is 6Pi.

You deserve to leave the answer together 6Pi and the inquiry is questioning for precise answer and not a decimal answer.

Question: can you work out the one of a circle of radius 6cm in ax of Pi?

Answer: First dual the radius to offer the diameter the the one (6 doubled is 12).

Now multiply this answer by Pi, to give an answer of 12Pi (you dont should work it out together the question wants the price in terms of Pi).

Question: how do you discover a surface area that a sphere as soon as the radius is 100?

Answer: Square the radius i m sorry is 10000, and also multiply by 4Pi to provide 40000Pi.


Question: What is the area of this quarter circle of radius 8 cm?

Answer: first square the radius to offer 64 and multiply it by Pi (3.14) to give 201.06...


Now divide 201.06 by 4 to provide 50.3 cm^2 rounded come 1 decimal place.

Question: The one of a one is 18π inches, so what is the area in terms v π?

Answer: divide the 18π through π to offer the diameter of the circle which provides 18.

Half 18 to provide a radius the 9.

Now usage πr^2 to offer the area which pertains to 81π .

Question: have the right to you occupational out the area of a semicircle through a radius 3cm?

Answer: Square the radius to give 9.

Multiply by Pi to give 28.274...

Now divide this price by 2 to offer 14.1cm^2 rounded come 1 decimal place.

(Divide by 2 since a semicircle is fifty percent the area the a circle.)

Question: A circle has circumference 27cm. What is the area of the circle? (use 3.14 for pi)

Answer: very first divide the circumference by Pi to give the diameter the the one (27 separated by 3.14 = 8.59...).

Now halve the diameter to give the radius (8.59 separated by 2 is 4.29...).


Now usage Pi*r^2 to discover the area the the one (Pi time 4.29^2 = 58.0 cm^2 to 1 decimal place).

Question: The diameter that a circle is 3.3, what is the area?


Answer: very first half the diameter the the circle to provide the radius which is 1.65.

Now square the raidus and also multiply the by 3.14 to provide the final answer (8.55 come 2 decimal places).

Question: What is the perimeter the a semi-circle v diameter that 86cm? create the answer as an expression in terms of π?

Answer: an initial multiply the diameter by Pi to give 86π.

Next fifty percent 86π to give 43π (this is the arc length).

Next add on the diameter to provide a last expression that 43π + 86.

Question: What is the area that a circle whose diameter is 10cm?

Answer: first half the diameter (10) to offer the radius, so 10 separated by 2 is 5.

Now square the radius which is 25 (5^2)

Now main point 25 through Pi to offer 25Pi.

If you desire your answer as a decimal climate multiply 25 by 3.14 to provide 78.5 come 1 decimal place.


Question: exactly how do you job-related out the area of a circle using the diameter and get the prize in Pi?

Answer: very first half the diameter the the circle to give the radius.

Next square the radius.

The last step is to multiply the radius by Pi, but because you desire the answer in terms of Pi put the number to the last step complied with by Pi.

Question: What is the area (in terms of pi) that a circle v a radius the 13?

Answer: an initial square 13 i beg your pardon is 169, and also then multiply the answer by Pi to give 169Pi.


Question: discover the area of a circle v a radius that 15cm? give your answer in terms of pi?

Answer: Square the radius and also multiply through Pi. 15^2 is 225, so the price is 225Pi. Just leave the pi space the finish of the number.

Question: uncover the area that a circle through diameter, d = 8m. Offer your answer in regards to π ?

Answer: an initial divide 8 by 2 to give a radius the 4m.

Now square 4 to offer 16, and multiply 16 by π to give 16π m^2.

Question: deserve to you work-related out the perimeter the a semicircle with a radius of 4?


Answer: First twin the radius to give 8, currently multiply this through Pi to give 8Pi. Now half 8Pi to give 4Pi.

So the size of the arc is 4Pi.

Now include on the diameter to provide a final answer that 4Pi + 8.

Question: The area of a circle, in terms of π , is 4π m squared. Discover the value of the radius?

Answer: an initial divide the area through Pi to give 4.

Next square root the radius to provide 2.

Comments

klordy on in march 26, 2013:

thx the really helped my boy with hmework

Augustine A Zavala native Texas on march 30, 2011:

Very informative. Thank you because that sharing.

Husky1970 on in march 29, 2011:

If you have actually a certain linear quantity of boundary and also want to enclose the biggest area possible with it, what should you do? say you have 100 feet that fence and want to enclose the biggest area possible.

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