Mark, a mathematics enthusiast, loves writing tutorials because that stumped students and also those who need to brush increase on their math skills.
You are watching: Leave your answer in terms of pi
In this article, ns will show you exactly how to find the area the a circle and express your answer in terms of pi (π). First, you'll need to familiarize yourself through the formula because that calculating the area that a circle:
A = π * r²
Let's specify our variables:
A: area of the circleπ: pi (a mathematical constant that is around equal come 3.141492 . . .)r: radius that the one (the distance from the circle's center allude to that edge)Typically, to uncover the area of a circle, we would simply plug in the circle's radius because that r and also 3.141592 because that π. If so, our answer would certainly be a number.
How do You Get an answer in regards to pi (π)?
To express your answer in terms of pi, simply refrain native substituting pi's numerical value for its symbol in the equation. The way, your answer will certainly look prefer xπ where x is whatever number you come increase with, and π is just a placeholder because that pi's worth (3.141582 . . .). Essentially, through expressing your answer in terms of pi, you room cutting one step out of your calculation. Let's take a watch at part examples.
Example problems With Processes and also Solutions
In every of the following example problems, we'll occupational through the procedure of detect a circle's area in regards to pi using just its radius or diameter.
Example 1
Work out the area that a circle that has a radius of 7 m. Give your answer in regards to 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 prior to pi and also put her answer in regards to the appropriate units squared).
Example 2
Work out the area of one that has a diameter that 22 cm. Offer your price in regards to pi.
This time, the diameter (the street all the way across the circle, or twice its radius) is given, for this reason we'll must halve this to provide 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 final answer is 121π cm² (put the number before pi and also put her answer in terms of the appropriate units squared).
This circular lawn has actually a radius of 13m, therefore our answer with be in meter squared.
Example 3
Work the end the area of the one lawn presented in the image above. Offer your price in terms of pi.
The radius of this lawn is 13 m, so we'll need to plug this value right 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 prior to pi and also put her answer in regards to the pertinent units squared).
This contents is accurate and also true to the finest of the author’s knowledge and is not intended to substitute for formal and individualized advice native a qualified professional.
Questions & Answers
Question: deserve to you work-related out the perimeter of a semicircle through a radius the 3cm? give your prize in terms of pi?
Answer: To occupational out the cirumference main point the diameter through pi.
The diameter is 6, and also so 6 multiply by Pi is 6Pi.
You can leave the answer together 6Pi and the question is questioning for specific answer and also not a decimal answer.
Question: have the right to you occupational out the one of a circle of radius 6cm in hatchet of Pi?
Answer: First dual the radius to offer the diameter that the circle (6 doubled is 12).
Now multiply this answer by Pi, to give response of 12Pi (you dont must work the out together the question wants the answer in regards to Pi).
Question: just how do you uncover a surface ar area the a sphere when the radius is 100?
Answer: Square the radius i beg your pardon is 10000, and also multiply by 4Pi to offer 40000Pi.
Question: What is the area that this 4 minutes 1 circle the radius 8 cm?
Answer: an initial square the radius to offer 64 and also multiply the by Pi (3.14) to give 201.06...
Now divide 201.06 by 4 to offer 50.3 cm^2 rounded to 1 decimal place.
Question: The one of a circle is 18π inches, for this reason what is the area in terms through π?
Answer: division the 18π through π to give the diameter of the one which gives 18.
Half 18 to provide a radius the 9.
Now use πr^2 to provide the area which pertains to 81π .
Question: have the right to you occupational out the area the a semicircle with a radius 3cm?
Answer: Square the radius to give 9.
Multiply by Pi to offer 28.274...
Now division this prize by 2 to offer 14.1cm^2 rounded to 1 decimal place.
(Divide by 2 due to the fact that a semicircle is half the area of a circle.)
Question: A circle has actually circumference 27cm. What is the area that the circle? (use 3.14 because that pi)
Answer: very first divide the circumference by Pi to offer the diameter that the one (27 split by 3.14 = 8.59...).
Now halve the diameter to offer the radius (8.59 split by 2 is 4.29...).
Now use Pi*r^2 to uncover the area the the circle (Pi times 4.29^2 = 58.0 cm^2 come 1 decimal place).
Question: The diameter of a one is 3.3, what is that area?
Answer: first half the diameter of the circle to give the radius i m sorry is 1.65.
Now square the raidus and multiply the by 3.14 to provide the last answer (8.55 come 2 decimal places).
Question: What is the perimeter of a semi-circle v diameter that 86cm? create the answer as an expression in regards to π?
Answer: first multiply the diameter by Pi to offer 86π.
Next fifty percent 86π to offer 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: very first half the diameter (10) to provide the radius, for this reason 10 separated by 2 is 5.
Now square the radius i beg your pardon is 25 (5^2)
Now multiply 25 by Pi to give 25Pi.
If you want your answer together a decimal climate multiply 25 through 3.14 to offer 78.5 to 1 decimal place.
Question: exactly how do you work out the area of a circle making use of the diameter and also get the answer in Pi?
Answer: first half the diameter the the circle to offer the radius.
Next square the radius.
The last step is to main point the radius by Pi, but because you desire the price in regards to Pi placed the number to the last step complied with by Pi.
Question: What is the area (in regards to pi) that a circle v a radius of 13?
Answer: first square 13 which is 169, and then main point the price by Pi to give 169Pi.
Question: discover the area the a circle through a radius the 15cm? offer your price in terms of pi?
Answer: Square the radius and also multiply by Pi. 15^2 is 225, so the answer is 225Pi. Just leave the pi room the end of the number.
Question: find the area the a circle through diameter, d = 8m. Offer your price in terms of π ?
Answer: an initial divide 8 by 2 to offer a radius that 4m.
Now square 4 to give 16, and multiply 16 by π to give 16π m^2.
Question: have the right to you work out the perimeter that a semicircle v a radius that 4?
Answer: First twin the radius to provide 8, currently multiply this through Pi to offer 8Pi. Now fifty percent 8Pi to provide 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 value of the radius?
Answer: very first divide the area by Pi to offer 4.
Next square root the radius to provide 2.
Comments
klordy on march 26, 2013:
thx the really helped my son with hmework
Augustine A Zavala indigenous Texas on in march 30, 2011:
Very informative. Say thanks to you for sharing.
Husky1970 on march 29, 2011:
If you have actually a specific linear amount of boundary and also want come enclose the greatest area feasible with it, what have to you do? say you have actually 100 feet that fence and also want come enclose the best area possible.
See more: How Many Liters In A Microliter To Liter, 1 Microliter (Μl Mcl) = 0
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Mark
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