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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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โˆ™ 2016-04-03 19:16:05
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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?


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.

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

The circumference of a circle is the radius times 2 times the irrational number "pi", which is approximately 3.14159. "Irrational" means that the number cannot be calculated as a ratio or fraction, and that the sequence of decimal places never repeats. So, the circumference of a circle of radius 9 is 56.55. If you had said that the radius of the circle was 9.0, we could reasonably calculate this to another couple of decimal places, but since the original number wasn't specified to 2 digits of precision, it's not reasonable to try to be more precise in the calculation.

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.

How do you find the circumference of a circle when the raduis is a fraction?

The circumference is 2*pi*radius (not raduis) and this formula is applicable whether the radius is an integer, a fraction, or even an irrational number.

Why did they name this irrational number pi?

Because it is the ratio of the perimeter of a circle to its radius. pi is the Greek letter which is the first letter for perimeter.

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