Question
The spoke of a wheel reaches from the center of the wheel to its rim. If the circumference of the rim of the wheel is 42 inches, how long is each spoke? Round your answer to the nearest hundredth.
Question 1 options:
A)
7 inches
B)
6.69 inches
C)
13.38 inches
D)
6.25 inches
Question 1 options:
A)
7 inches
B)
6.69 inches
C)
13.38 inches
D)
6.25 inches
Answers
GPT-4o mini
To find the length of each spoke, we need to determine the radius of the wheel. The spoke of the wheel extends from the center to the rim, which is the radius.
The circumference \( C \) of a circle is related to its radius \( r \) by the formula:
\[
C = 2\pi r
\]
Given that the circumference of the rim is 42 inches, we can set up the equation:
\[
42 = 2\pi r
\]
Now, we can solve for \( r \):
\[
r = \frac{42}{2\pi} = \frac{21}{\pi}
\]
Using \( \pi \approx 3.14 \):
\[
r \approx \frac{21}{3.14} \approx 6.69 \text{ inches}
\]
Thus, each spoke is approximately 6.69 inches long.
Rounding to the nearest hundredth, we find:
**Answer: B) 6.69 inches**
The circumference \( C \) of a circle is related to its radius \( r \) by the formula:
\[
C = 2\pi r
\]
Given that the circumference of the rim is 42 inches, we can set up the equation:
\[
42 = 2\pi r
\]
Now, we can solve for \( r \):
\[
r = \frac{42}{2\pi} = \frac{21}{\pi}
\]
Using \( \pi \approx 3.14 \):
\[
r \approx \frac{21}{3.14} \approx 6.69 \text{ inches}
\]
Thus, each spoke is approximately 6.69 inches long.
Rounding to the nearest hundredth, we find:
**Answer: B) 6.69 inches**