Question

Da circumferences of a circle is 22 x inches. Find da area of dat circle. Substitute 3.14 for pi. Express ur answer to da hundredths place

Answer 1

To find the area of the circle given the circumference, we can follow these steps:

1. **Write the formula for circumference**:

\[
C = 2\pi r
\]

where \( C \) is the circumference and \( r \) is the radius.

2. **Substitute the given value of circumference**:

\[
22x = 2\pi r
\]

3. **Solve for the radius \( r \)**:

\[
r = \frac{22x}{2\pi} = \frac{22x}{2 \times 3.14} = \frac{22x}{6.28}
\]

Simplifying this gives:

\[
r = \frac{11x}{3.14}
\]

4. **Write the formula for area**:

\[
A = \pi r^2
\]

5. **Substitute the value of \( r \) into the area formula**:

\[
A = \pi \left(\frac{11x}{3.14}\right)^2
\]

6. **Calculate \( r^2 \)**:

\[
r^2 = \left(\frac{11x}{3.14}\right)^2 = \frac{121x^2}{9.8596}
\]

(where \( 9.8596 = 3.14^2\))

7. **Now substitute this back into the area formula**:

\[
A = \pi \cdot \frac{121x^2}{9.8596}
\]

Substituting \( \pi = 3.14 \):

\[
A = 3.14 \cdot \frac{121x^2}{9.8596}
\]

8. **Calculate the area**:

First, calculate \( 3.14 \times 121 \):

\[
3.14 \times 121 = 379.94
\]

Now, divide by \( 9.8596 \):

\[
A = \frac{379.94x^2}{9.8596} \approx 38.49x^2
\]

Therefore, the area of the circle is approximately:

\[
\boxed{38.49x^2} \text{ square inches}
\]