Question

The circumference of a circle is 30t. What is its area? ​

Answer 1

`A=(225t^2)/(\pi)` given the circumference is 30t.

Explanation:

The circumference of a circle is
`C=2\pi r` and the area of a circle is
`A=\pi r^2` assuming the radius is
`r` for the circle in question.

We are given the circumference of our circle is
`2 \pi r=30t`.

If we solve this for r we get:
`r=(30t)/(2\pi)`. To get this I just divided both sides by
`2\pi` since this was the thing being multiplied to
`r`.

So now the area is
`A=\pi r^2=\pi ((30t)/(2 \pi))^2`.

Simplifying this:

`A=\pi ((30t)/(2 \pi))^2`.

30/2=15 so:

`A=\pi ((15t)/(\pi))^2`.

Squaring the numerator and the denominator:

`A=\pi (((15t)^2)/((\pi)^2)`

Using law of exponents or seeing that a factor of
`\pi` cancels:

`A=((15t)^2)/(\pi)`

`A=(15^2t^2)/(\pi)`

`A=(225t^2)/(\pi)`