what is the ratio of the area of a circle to the square of its radius?
The area of a circle is given as the product of pi and square of its radius, that is:
Area of circle = `pi*r^2`
where, r is the radius of the circle.
Thus the ratio of area of a circle to the square of its radius would be equal to pi. That is:
`(area)/r^2 = pi`
The formula for the area of a circle is A = Π r2 . The square of a circle's radius can be represented as as r2. We can arbitrarily choose to use the variable R to represent the square of the circle's radius. (The particular letter you choose to use is up to you). We can then say two things:
1. R = r2 and,
2. the ratio of a circle's area to the square of that circle's radius is equal to A/R.
A/R, in turn, is in turn equal to Π r2/ r2 . (Here we've simply substituted the previous equations.) In other words, `A/R =(Pirˆ2)/(rˆ2)`
The r2 in the numerator cancels with that in the denominator, so the equation becomes `A/R =Pi`
Thus, the ratio of a circle's area to the square of that circle's radius is equal to `Pi.`