Geometry

# Why the area of a circle with a rational radius must be an irrational number?

###### Wiki User

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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## Related Questions

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.

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

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.

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.

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

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

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.

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.

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.

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.

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.

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.

Circumference = 2 times pi times radius. Circumference of a circle is the distance along the edge of the circle. Radius is the distance from the center of the circle to the edge. Pi is the ratio that was derived from relationships in dimensions of circles. It is an irrational number; its value is approximately 3.1416

I guess you mean of a circle: area_circle = &pi; x radius2 circumference_circle = 2 x &pi; x radius &pi; is the ratio of the diameter to circumference of any circle, is an irrational number and starts 3.14159265...

The question is assumed to be asking whether the area of a circle can "come out even", or be written as an exact number without rounding or approximating. The answer is yes ... but then the radius (or circumference) of the circle couldn't be perfectly written. Look at it this way: We know that 'pi' is the constant that relates the area of a circle to its diameter: A = (pi)R2. You can re-write this simple formula as: A/R2 = pi. Since 'pi' is an irrational number, then the fraction A/R2 is an irrational number, meaning that either 'A' or 'R2' (or both) must be irrational.

A = Pi X R2, where Pi = the irrational form best known as 3.14 or 22/7, and R = the radius of the circle.

Circumference = 2*pi*r where r is the radius and pi is an irrational number which is approx equal to 3.14.So, 31.4 = 2*3.14*r so that r = 5 metres.

The area of the (inside) of a circle - the circle itself is a line with no area - is calculated by:pi * r2the perimeter - also called the circumference is the length around the circle and is calculated:2 * pi * rwhere "r" is the radius, the distance from the center to the edge of the circle and "pi" is the irrational number 3.14159....

The area of a circle is the radius "r" squared times the irrational number pi (approximately 3.14)so a 14-foot diameter means a 7 foot radius.(7 ^2) * 3.14 = 49 * 3.14 = 153.86 square feet.

The area of any circle is (pi) x (radius)2 .The area of half the circle is just half of that number.

No, that process gives you the circumference of the circle.To find the area of a circle, multiply 3.14 by the square of the radius.Notes:1). The square of the radius means (radius) times (radius).2). The number "3.14" is not exact. It's an approximation for the number "pi".

Many things. In math? Rational or Radius

The diameter of a circle is twice the radius.The diameter of a circle is twice the radius.The diameter of a circle is twice the radius.The diameter of a circle is twice the radius.

That would depend on its radius because the area of a circle is pi times radius squared