Question

the circumference of a circle is 81.64 inches what is the area in square inches use 3.14 and round to the nearest tenth is necessary

Answer 1

To calculate the area of the circle given its circumference, we can use the formulas for circumference and area. The formulas are:

1. Circumference \( C = 2\pi r \)
2. Area \( A = \pi r^2 \)

First, we need to find the radius \( r \) from the given circumference \( C = 81.64 \) inches.

Using the circumference formula:

\[
C = 2\pi r
\]

Substituting the value of \( C \):

\[
81.64 = 2 \times 3.14 \times r
\]

Now, we can solve for \( r \):

\[
81.64 = 6.28r
\]

\[
r = \frac{81.64}{6.28} \approx 13.0 \text{ inches}
\]

Now that we have the radius, we can find the area using the area formula:

\[
A = \pi r^2
\]

Substituting \( r \) and using \( \pi \approx 3.14 \):

\[
A = 3.14 \times (13.0)^2
\]

Calculating \( (13.0)^2 \):

\[
(13.0)^2 = 169.0
\]

Now, plug that back into the area formula:

\[
A = 3.14 \times 169.0 \approx 530.46
\]

Finally, rounding to the nearest tenth:

\[
A \approx 530.5 \text{ square inches}
\]

So, the area of the circle is approximately **530.5 square inches**.