Question
A large clock on a county courthouse has a circumference of about 25 feet. The minute hand extends from the center of the clock to the edge of the clock. How long is the minute hand? Round to the nearest tenth. Use 3.14 for π.
Answers
GPT-4o mini
To find the length of the minute hand, we can first determine the radius of the clock using the circumference. The formula for the circumference \( C \) of a circle is given by:
\[
C = 2\pi r
\]
where \( r \) is the radius. We are given that the circumference \( C \) is approximately 25 feet. We can rearrange the formula to solve for \( r \):
\[
r = \frac{C}{2\pi}
\]
Substituting in the given values:
\[
r = \frac{25}{2 \times 3.14}
\]
Calculating the denominator:
\[
2 \times 3.14 = 6.28
\]
Now substituting back to find \( r \):
\[
r = \frac{25}{6.28} \approx 3.976
\]
To round to the nearest tenth:
\[
r \approx 4.0 \text{ feet}
\]
Since the minute hand extends from the center of the clock to the edge, the length of the minute hand is equal to the radius of the clock. Therefore, the length of the minute hand is approximately:
\[
\boxed{4.0} \text{ feet}
\]
\[
C = 2\pi r
\]
where \( r \) is the radius. We are given that the circumference \( C \) is approximately 25 feet. We can rearrange the formula to solve for \( r \):
\[
r = \frac{C}{2\pi}
\]
Substituting in the given values:
\[
r = \frac{25}{2 \times 3.14}
\]
Calculating the denominator:
\[
2 \times 3.14 = 6.28
\]
Now substituting back to find \( r \):
\[
r = \frac{25}{6.28} \approx 3.976
\]
To round to the nearest tenth:
\[
r \approx 4.0 \text{ feet}
\]
Since the minute hand extends from the center of the clock to the edge, the length of the minute hand is equal to the radius of the clock. Therefore, the length of the minute hand is approximately:
\[
\boxed{4.0} \text{ feet}
\]