Question

Find da area of a circle given C = 4x Given ur answer in terms of x

Answer 1

To find the area of a circle given its circumference \( C = 4x \), we can follow these steps:

1. **Use the formula for the circumference of a circle**:
\[
C = 2\pi r
\]
Given that \( C = 4x \), we can set up the equation:
\[
4x = 2\pi r
\]

2. **Solve for the radius \( r \)**:
Divide both sides by \( 2\pi \):
\[
r = \frac{4x}{2\pi} = \frac{2x}{\pi}
\]

3. **Use the formula for the area of a circle**:
\[
A = \pi r^2
\]
Substitute the expression for \( r \):
\[
A = \pi \left(\frac{2x}{\pi}\right)^2
\]

4. **Simplify the area**:
\[
A = \pi \left(\frac{4x^2}{\pi^2}\right) = \frac{4x^2}{\pi}
\]

Therefore, the area of the circle in terms of \( x \) is:
\[
A = \frac{4x^2}{\pi}
\]