The circumference of a circle is 15pi centimeters . In cm^2, what is the area of the circle in terms of pi

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!

The circumference of a circle is 15pi centimeters. In cm^2, what is the area of the circle in terms of pi?

Learn how to calculate the area of a circle when the circumference is given as 15π centimeters. This step-by-step guide uses key geometric concepts, including the formulas for circumference and area. Perfect for students in Grades 6-8.

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