Question

How do you find the circumference and area of the circle whose equation is `x^2+y^2=36`?

Answer 1

Circumference = `12 pi`.
Area = `36 pi`.

Explanation:

The equation of a circle centred in the origin having radius r is `x^2 + y^2 = r^2`. Comparing with the equation of the given circle, we get `r^2 = 36 => r = 6`. (Since `r > 0`.)

Note that all we need to calculate the area and circumference of a circle is the radius. Now we can use the formulae known to calculate the required values.

Circumference = `2 pi r = 2 pi * 6 = 12 pi`.
Area = `pi r^2 = 36 pi`.