Let's solve the problem step-by-step.
1. Understand the Given Information:
- The circumference of the rim of the wheel is given as 27 inches.
- We need to find the length of each spoke, which is essentially the radius of the wheel.
2. Relationship Between Circumference and Radius:
- The circumference [tex]\( C \)[/tex] of a circle is given by the formula:
[tex]\[ C = 2 \pi r \][/tex]
where [tex]\( r \)[/tex] is the radius of the circle and [tex]\( \pi \)[/tex] (pi) is approximately 3.14159.
3. Rearrange the Formula to Solve for the Radius:
- We need to solve for [tex]\( r \)[/tex] (the radius). Rearranging the formula, we get:
[tex]\[ r = \frac{C}{2 \pi} \][/tex]
4. Substitute the Given Circumference:
- Substitute the circumference value (27 inches) into the formula:
[tex]\[ r = \frac{27}{2 \pi} \][/tex]
5. Calculate the Radius:
- When we divide 27 by [tex]\( 2 \pi \)[/tex], we get:
[tex]\[ r \approx 4.297183463481174 \][/tex]
6. Round the Radius to the Nearest Hundredth:
- Rounding 4.297183463481174 to the nearest hundredth, we get:
[tex]\[ r \approx 4.30 \][/tex]
Hence, the length of each spoke, rounded to the nearest hundredth, is approximately 4.30 inches. Therefore, the correct answer is:
O A. 4.30
