The formula for the circumference of a circle is:

$C = 2\pi r$

where $r$ is the radius of the circle. Given that the circumference is $15\pi$ cm, we can set up the equation:

$2\pi r = 15\pi$

Now, solve for $r$ by dividing both sides by $2\pi$:

$r = \frac{15\pi}{2\pi} = \frac{15}{2} = 7.5 \, \text{cm}$

Next, use the formula for the area of a circle, which is:

$A = \pi r^2$

Substitute $r = 7.5$ into the formula:

$A = \pi (7.5)^2 = \pi (56.25) = 56.25\pi \, \text{cm}^2$

Thus, the area of the circle is:

$A = 56.25\pi \, \text{cm}^2$

Do you need more details or have any questions?

Here are 5 related questions to deepen your understanding:

1. What is the formula for the diameter of a circle if the radius is known?
2. How would the area change if the radius were doubled?
3. If the area of a circle is given, how do you calculate the radius?
4. Can you derive the formula for the area of a circle from the circumference?
5. How do you calculate the volume of a sphere using its radius?

Tip: Remember, the radius is always half the diameter!