Question

The area of one side of a U.S. 50-cent piece is 735 square millimeters. What is the diameter of the half-dollar, rounded to the nearest tenth. Use 3.14 for the value of π. The diameter = _______ mm.

30.6

15.3

182.5

234.1

Answer 1

To find the diameter of the half-dollar coin based on the area of one side, we can use the formula for the area of a circle:

\[
A = \pi r^2
\]

where \(A\) is the area and \(r\) is the radius. We can rearrange this formula to solve for the radius:

\[
r^2 = \frac{A}{\pi}
\]
\[
r = \sqrt{\frac{A}{\pi}}
\]

Given that the area \(A\) is 735 square millimeters and using \( \pi \approx 3.14 \):

\[
r = \sqrt{\frac{735}{3.14}}
\]

Calculating the right-hand side:

\[
\frac{735}{3.14} \approx 234.2
\]

Now, taking the square root:

\[
r \approx \sqrt{234.2} \approx 15.3 \text{ mm}
\]

The diameter \(d\) is twice the radius:

\[
d = 2r \approx 2 \times 15.3 \approx 30.6 \text{ mm}
\]

Thus, rounding to the nearest tenth, the diameter of the half-dollar is

\[
\boxed{30.6} \text{ mm}.
\]