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

Write your answer...

Submit

Still have questions?

Continue Learning about Geometry

Technically there are an infinite number of radii in a circle. A radius is a line from the center of the circle to a point on its edge, and since there are an infinite number of points on a circle's edge there are an infinite number of radii.

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

The radius of the circle.

The radius of a circle or a sphere has infinite number of points.

The distance from the center of a circle to any point on the circle is called the radius of the circle. The radius is a line segment that starts at the center of the circle and ends at any point on the circle. It is always a straight line and is always perpendicular to the circumference of the circle. The radius is half the diameter of the circle, which is the distance across the circle through the center. The diameter of a circle is always twice the length of the radius. My recommendation ʜᴛᴛᴘꜱ://ᴡᴡᴡ.ᴅɪɢɪꜱᴛᴏʀᴇ24.ᴄᴏᴍ/ʀᴇᴅɪʀ/372576/ꜱᴀɪᴋɪʀᴀɴ21ᴍ/

Related questions

Maybe

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.

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.

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.

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

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.

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.