Mark, a math enthusiast, loves writing tutorials for stumped students and those who need to brush up on their math skills.
In this article, I will show you how to find the area of a circle and express your answer in terms of pi (π). First, you'll need to familiarize yourself with the formula for calculating the area of a circle:
A = π * r²
Let's define our variables:
- A: area of the circle
- π: pi (a mathematical constant that is approximately equal to 3.141492 . . .)
- r: radius of the circle (the distance from the circle's center point to its edge)
Typically, to find the area of a circle, we would simply plug in the circle's radius for r and 3.141592 for π. If so, our answer would be a number.
How Do You Get an Answer in Terms of pi (π)?
To express your answer in terms of pi, simply refrain from substituting pi's numerical value for its symbol in the equation. That way, your answer will look like xπ where x is whatever number you come up with, and π is simply a placeholder for pi's value (3.141582 . . .). Essentially, by expressing your answer in terms of pi, you are cutting one step out of your calculation. Let's take a look at some examples.
Example Problems With Processes and Solutions
In each of the following example problems, we'll work through the process of finding a circle's area in terms of pi using only its radius or diameter.
Work out the area of a circle that has a radius of 7 m. Give your answer in terms of pi.
All you need 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 terms of the relevant units squared).
Work out the area of circle that has a diameter of 22 cm. Give your answer in terms of pi.
This time, the diameter (the distance all the way across the circle, or twice its radius) is given, so we'll need to halve this to give the radius. Since 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 final answer is 121π cm² (put the number before pi and put your answer in terms of the relevant units squared).
Work out the area of the circular lawn shown in the image above. Give your answer in terms of pi.
The radius of this lawn is 13 m, so 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 final answer is 169π m² (put the number before pi and put your answer in terms of the relevant units squared).
This content is accurate and true to the best of the author’s knowledge and is not meant to substitute for formal and individualized advice from a qualified professional.
Questions & Answers
Question: Can you work out the perimeter of a semicircle with a radius of 3cm? Give your answer in terms of pi?
Answer: To work out the cirumference multiply the diameter by pi.
The diameter is 6, and so 6 multiplied by Pi is 6Pi.
You can leave the answer as 6Pi and the question is asking for an exact answer and not a decimal answer.
Question: Can you work out the circumference of a circle of radius 6cm in term of Pi?
Answer: First double the radius to give the diameter of the circle (6 doubled is 12).
Now multiply this answer by Pi, to give an answer of 12Pi (you dont need to work it out as the question wants the answer in terms of Pi).
Question: How do you find a surface area of a sphere when the radius is 100?
Answer: Square the radius which is 10000, and multiply by 4Pi to give 40000Pi.
Question: What is the area of this quarter circle of radius 8 cm?
Answer: First square the radius to give 64 and multiply it by Pi (3.14) to give 201.06...
Now divide 201.06 by 4 to give 50.3 cm^2 rounded to 1 decimal place.
Question: The circumference of a circle is 18π inches, so what is the area in terms with π?
Answer: Divide the 18π by π to give the diameter of the circle which gives 18.
Half 18 to give a radius of 9.
Now use πr^2 to give the area which comes to 81π .
Question: Can you work out the area of a semicircle with a radius 3cm?
Answer: Square the radius to give 9.
Multiply by Pi to give 28.274...
Now divide this answer by 2 to give 14.1cm^2 rounded to 1 decimal place.
(Divide by 2 because a semicircle is half the area of a circle.)
Question: A circle has circumference 27cm. What is the area of the circle? (use 3.14 for pi)
Answer: First divide the circumference by Pi to give the diameter of the circle (27 divided by 3.14 = 8.59...).
Now halve the diameter to give the radius (8.59 divided by 2 is 4.29...).
Now use Pi*r^2 to find the area of the circle (Pi times 4.29^2 = 58.0 cm^2 to 1 decimal place).
Question: The diameter of a circle is 3.3, what is that area?
Answer: First half the diameter of the circle to give the radius which is 1.65.
Now square the raidus and multiply it by 3.14 to give the final answer (8.55 to 2 decimal places).
Question: What is the perimeter of a semi-circle with diameter of 86cm? Write the answer as an expression in terms of π?
Answer: First multiply the diameter by Pi to give 86π.
Next half 86π to give 43π (this is the arc length).
Next add on the diameter to give a final expression of 43π + 86.
Question: What is the area of a circle whose diameter is 10cm?
Answer: First half the diameter (10) to give the radius, so 10 divided by 2 is 5.
Now square the radius which is 25 (5^2)
Now multiply 25 by Pi to give 25Pi.
If you want your answer as a decimal then multiply 25 by 3.14 to give 78.5 to 1 decimal place.
Question: How do you work out the area of a circle using the diameter and get the answer in Pi?
Answer: First half the diameter of the circle to give the radius.
Next square the radius.
The final step is to multiply the radius by Pi, but since you want the answer in terms of Pi put the number to the last step followed by Pi.
Question: What is the area (in terms of pi) of a circle with a radius of 13?
Answer: First square 13 which is 169, and then multiply the answer by Pi to give 169Pi.
Question: Find the area of a circle with a radius of 15cm? Give your answer in terms of pi?
Answer: Square the radius and multiply by Pi. 15^2 is 225, so the answer is 225Pi. Just leave the pi are the end of the number.
Question: Find the area of a circle with diameter, d = 8m. Give your answer in terms of π ?
Answer: First divide 8 by 2 to give a radius of 4m.
Now square 4 to give 16, and multiply 16 by π to give 16π m^2.
Question: Can you work out the perimeter of a semicircle with a radius of 4?
Answer: First double the radius to give 8, now multiply this by Pi to give 8Pi. Now half 8Pi to give 4Pi.
So the length of the arc is 4Pi.
Now add on the diameter to give a final answer of 4Pi + 8.
Question: The area of a circle, in terms of π , is 4π m squared. Find the value of the radius?
Answer: First divide the area by Pi to give 4.
Next square root the radius to give 2.
klordy on March 26, 2013:
thx it really helped my son with hmework
Augustine A Zavala from Texas on March 30, 2011:
Very informative. Thank you for sharing.
Husky1970 on March 29, 2011:
If you have a certain linear quantity of boundary and want to enclose the greatest area possible with it, what should you do? Say you have 100 feet of fence and want to enclose the greatest area possible.