Question

A wall clock has a circumference of 43.96 inches. What is the area of the clock? (Use 3.14 for pie.)
A.
87.92 square inches
B.
153.86 square inches
C.
21.98 square inches
D.
307.72 square inches

Answer 1

To find the area of the wall clock, we need to first find the radius from the circumference. The formula for the circumference \( C \) of a circle is given by:

\[
C = 2\pi r
\]

where \( r \) is the radius and \( \pi \) is approximately 3.14. We can rearrange this formula to solve for \( r \):

\[
r = \frac{C}{2\pi}
\]

Substituting the given circumference (43.96 inches) into the equation:

\[
r = \frac{43.96}{2 \times 3.14}
\]
\[
r = \frac{43.96}{6.28}
\]
\[
r = 7.0032 \text{ inches} \quad (\text{approximately } 7 \text{ inches})
\]

Now, we can use the radius to find the area \( A \) of the circle using the area formula:

\[
A = \pi r^2
\]

Substituting the value of \( r \):

\[
A = 3.14 \times (7.0032)^2
\]
\[
A = 3.14 \times 49.0454 \quad (\text{approximately } 7.0032^2 \text{ is } 49.0454)
\]
\[
A \approx 154.013 \text{ square inches}
\]

Rounding this to two decimal places, we get:

\[
A \approx 153.86 \text{ square inches}
\]

The correct answer is:

**B. 153.86 square inches**.