Mark, a mathematics enthusiast, loves writing tutorials for stumped students and also those who need to brush up on your math skills.

You are watching: Leave your answer in terms of pi


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In this article, ns will display you how to discover the area the a circle and also express her answer in regards to pi (π). First, you'll should familiarize yourself through the formula for calculating the area of a circle:


A = π * r²

Let's define our variables:

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

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

How perform You Get an answer in regards to pi (π)?

To express her answer in regards to pi, merely refrain native substituting pi's numerical worth for its price in the equation. The way, your answer will certainly look favor where x is whatever number you come up with, and also π is simply a placeholder for pi's value (3.141582 . . .). Essentially, through expressing your answer in terms of pi, you are cutting one step out of her calculation. Let's take a watch at some examples.


Example problems With Processes and also Solutions

In every of the following instance problems, we'll job-related through the process of recognize a circle's area in regards to pi using just its radius or diameter.

Example 1

Work out the area of a one that has a radius of 7 m. Offer your price in terms of pi.

All you have to 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 final answer is 49π m2 (put the number before pi and put your answer in regards to the pertinent units squared).

Example 2

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


This time, the diameter (the distance all the way across the circle, or double its radius) is given, so we'll have to halve this to give the radius. Due to the fact that the diameter is 22 cm, the radius is 11 cm, or fifty percent 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 prior to pi and also put your answer in regards to the relevant units squared).


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


Example 3

Work out the area of the circular lawn shown in the image above. Offer your answer in regards to pi.

The radius that this lawn is 13 m, for this reason we'll need 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 put her answer in terms of the pertinent units squared).

This content is accurate and also true come the best of the author’s knowledge and is not meant to substitute because that formal and individualized advice indigenous a qualified professional.


Questions & Answers

Question: have the right to you job-related out the perimeter of a semicircle with a radius of 3cm? provide your prize in regards to pi?

Answer: To job-related out the cirumference multiply the diameter by pi.

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

You can leave the answer as 6Pi and also the concern is questioning for specific answer and not a decimal answer.

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

Answer: First double the radius to give the diameter the the one (6 double is 12).

Now main point this prize by Pi, to give solution of 12Pi (you dont need to work it out together the inquiry wants the price in regards to Pi).

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

Answer: Square the radius i beg your pardon is 10000, and multiply by 4Pi to offer 40000Pi.


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

Answer: an initial square the radius to provide 64 and also multiply that by Pi (3.14) to give 201.06...


Now division 201.06 through 4 to offer 50.3 cm^2 rounded to 1 decimal place.

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

Answer: division the 18π through π to provide the diameter the the one which gives 18.

Half 18 to offer a radius that 9.

Now usage πr^2 to give the area which involves 81π .

Question: deserve to you work out the area that a semicircle v a radius 3cm?

Answer: Square the radius to offer 9.

Multiply through Pi to offer 28.274...

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

(Divide by 2 since a semicircle is half the area of a circle.)

Question: A circle has actually circumference 27cm. What is the area the the circle? (use 3.14 because that pi)

Answer: an initial divide the circumference by Pi to offer the diameter the the one (27 split by 3.14 = 8.59...).

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


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

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


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

Now square the raidus and multiply the by 3.14 to give the last answer (8.55 to 2 decimal places).

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

Answer: very first multiply the diameter by Pi to give 86π.

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

Next add on the diameter to provide a final expression of 43π + 86.

Question: What is the area of a circle who diameter is 10cm?

Answer: very first half the diameter (10) to provide the radius, therefore 10 divided by 2 is 5.

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

Now main point 25 by Pi to offer 25Pi.

If you want your answer together a decimal then multiply 25 by 3.14 to give 78.5 come 1 decimal place.


Question: just how do you work out the area of a circle making use of the diameter and also get the prize in Pi?

Answer: an initial half the diameter the the one to give the radius.

Next square the radius.

The last step is to main point the radius through Pi, but due to the fact that you desire the answer in regards to Pi put the number to the critical step followed by Pi.

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

Answer: first square 13 i beg your pardon is 169, and then multiply the prize by Pi to provide 169Pi.


Question: find the area that a circle with a radius that 15cm? give your price in regards to pi?

Answer: Square the radius and multiply through Pi. 15^2 is 225, therefore the price is 225Pi. Simply leave the pi are the finish of the number.

Question: uncover the area that a circle with diameter, d = 8m. Offer your answer in terms of π ?

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

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

Question: can you occupational out the perimeter that a semicircle through a radius the 4?


Answer: First dual the radius to offer 8, now multiply this by Pi to give 8Pi. Now fifty percent 8Pi to give 4Pi.

So the length of the arc is 4Pi.

Now add on the diameter to provide a last answer the 4Pi + 8.

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

Answer: very first divide the area through Pi to give 4.

Next square source the radius to give 2.

Comments

klordy on in march 26, 2013:

thx it really aided my child with hmework

Augustine A Zavala indigenous Texas on march 30, 2011:

Very informative. Say thanks to you because that sharing.

Husky1970 on march 29, 2011:

If you have actually a specific linear amount of boundary and also want come enclose the biggest area possible with it, what should you do? to speak you have 100 feet the fence and want come enclose the greatest area possible.

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