Question

A circular serving plate has a circumference of 37.68 inches. What is the area of the plate? Round to the nearest tenth. Use 3.14 for π.

Answer 1

To find the area of the circular serving plate, we can use the formulas for circumference and area of a circle.

1. **Find the radius** using the circumference formula:
\[
C = 2\pi r
\]
Given that the circumference \(C\) is 37.68 inches, we can solve for the radius \(r\):
\[
37.68 = 2 \times 3.14 \times r
\]
Rearranging the equation for \(r\):
\[
r = \frac{37.68}{2 \times 3.14}
\]
\[
r = \frac{37.68}{6.28} \approx 6.0 \text{ inches}
\]

2. **Calculate the area** using the area formula for a circle:
\[
A = \pi r^2
\]
Substituting the value of \(r\):
\[
A = 3.14 \times (6.0)^2
\]
\[
A = 3.14 \times 36
\]
\[
A = 113.04 \text{ square inches}
\]

Finally, rounding to the nearest tenth, the area of the plate is:
\[
\boxed{113.0} \text{ square inches}
\]