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

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.


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.


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


What is the area of the circle?

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


What is the area of a circle if the radius is 9m?

The area of a circle if the radius is 9m 254.5m2


What is the radius of a circle with the area of 36?

The radius of a circle with the area of 36 is 3.385


What is the area of a circle with the radius of 21?

The area of a circle of radius 21 is 1386


What is the area of circle with a radius of 35?

Area of a circle = pi*radius squared


What is the area of a circle with the radius of 14.4?

The area of a circle with a radius of 14.4 is 651.4


What is the area of a shaded circle with a radius of 135?

A circle with a radius of 135 units has an area of 57,255.53 square units.


What is the area of a circle of the radius of 10m?

A circle with a radius of 10m has an area of 314.16 m2