Question

A wall clock has a circumference of 37.68 inches. What is the area of the clock? (Use 3.14 for .)
A.
18.84 square inches
B.
75.36 square inches
C.
113.04 square inches
D.
226.08 square inches

Answer 1

To find the area of the clock, we can start with the formula for the circumference of a circle:

\[
C = 2\pi r
\]

where \( r \) is the radius and \( \pi \) is approximately 3.14. We have the circumference \( C = 37.68 \) inches.

First, we can solve for the radius \( r \):

\[
37.68 = 2 \times 3.14 \times r
\]

Dividing both sides by \( 2 \times 3.14 \):

\[
r = \frac{37.68}{2 \times 3.14}
\]

Calculating:

\[
r = \frac{37.68}{6.28} \approx 6
\]

Now that we have the radius, we can find the area \( A \) of the clock using the formula for the area of a circle:

\[
A = \pi r^2
\]

Substituting the values for \( \pi \) and \( r \):

\[
A = 3.14 \times (6)^2
\]

Calculating \( (6)^2 \):

\[
(6)^2 = 36
\]

Now we can find the area:

\[
A = 3.14 \times 36
\]

Calculating \( 3.14 \times 36 \):

\[
A = 113.04
\]

Thus, the area of the clock is:

\[
\boxed{113.04} \text{ square inches}
\]

So the correct answer is **C. 113.04 square inches**.