Question

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

Answer 1

Answer:

$A=\frac{225t^2}{\pi}$ given the circumference is 30t.

Step-by-step 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: $r=\frac{30t}{2\pi}$.  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 $A=\pi r^2=\pi (\frac{30t}{2 \pi})^2$.

Simplifying this:

$A=\pi (\frac{30t}{2 \pi})^2$.

30/2=15 so:

$A=\pi (\frac{15t}{\pi})^2$.

Squaring the numerator and the denominator:

$A=\pi (\frac{(15t)^2}{(\pi)^2}$

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

$A=\frac{(15t)^2}{\pi}$

$A=\frac{15^2t^2}{\pi}$

$A=\frac{225t^2}{\pi}$