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It the radius is r then the area is pi*r*r - which is pi times a rational number. pi is an irrational number, so the multiple of pi and a rational number is irrational.

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Q: Why the area of a circle with a rational radius must be an irrational number?
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Related questions

Can a circle with an irrational radius have a rational area?

Maybe


Is a radius of a circle that has 0.75 centimeters irrational or rational?

If 0.75 is the radius, that's rational. If 0.75 is the diameter, the radius is also rational: multiplying two rational numbers together always gives you a rational number.


Is the radius of a circle is irrational would the area must be irrational?

Yes and the area of any circle is an irrational number because its area is pi*radius squared whereas pi is an irrational number.


Does percents are rational or irrational?

It depends on the percentage. A 1 cm arc of a circle whose radius is 1 cm will represent 100*1/(2pi) % = 50/pi % and that is an irrational percentage. A semicircular arc of the same circle will represent 50%, which is rational.


Where are some places you can find irrational numbers?

Almost anywhere in geometry. If a circle has an rational radius, its circumference and area will be irrational. Conversely, if the area is rational then the radius will be irrational. The ratio of the diagonal of a square to its side is always sqrt(2) - an irrational. So if the sides are of rational length then the diagonal is irrational. There are lots of other common objects where the fact that some of the measures are rational forces other measures to be irrational. And circles and squares are all around you. Your glass / coffee mug is probably circular. Your plates, bowls etc. The ratio of the length to width of standard paper (A4) is irrational.


What is the relationship between the radius of a circle and its area?

area = pi*r2 where pi is the irrational number approximated by 3.14159


Is 1.7 the radius of a circle?

1.7 is a fine number. It can be the radius of a circle.Any number can be the radius of a circle.


What is the area of a circle with the radius of 6mm?

Area of a circle with radius r is pi*r2 where pi is the irrational number approximately equal to 3.14159. You now have all the information required to answer this and other similar questions.


How do you get a circumfrence of a circle?

The circumference of a circle can be found by multiplying its diameter (the distance from one point on the circle to its opposite point) by the irrational number pi. The value of pi is about 3.14, but it has an infinite number of nonrepeating digits. The circumference can also be expressed as 2(pi)r, where r is the radius. The radius is the distance from the center of the circle to any point on the circle. It is equal to half of the radius.


What is the circumference of a circle with the radius of 9?

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Why did they name this irrational number pi?

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What happens to the circumference of a circle if you triple the radius?

Since circumference is proportional to the diameter (the proportionality is the definition of the irrational number pi) and the radius is just twice the diameter, if you triple the radius, you also triple the circumference.


What is c equals 2ฯ€r?

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What is the area of the circle?

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Is there a way to perfectly define the area of a circle?

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What number does r stand for?

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What is the radius of a circle that has a circumference of 31.4 meters?

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What is the radius of a circle where d is the diameter of the circle?

the radius of a circle is r


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The radius of a circle is half the circle's diameter