Question

1. a team in science class placed a chalk mark on the side of a wheel and rolled the wheel in a straight line until the chalk mark returned to the same position. the team then measured the distance the wheel had rolled and found it to be 35 cm. to the nearest tenth, what is the area of the wheel?

options:
○ 27.5 cm²
○ 97.5 cm²
○ 390.1 cm²
○ 195.1 cm²

Explanation:

Step1: Identify the circumference

The distance rolled until the chalk mark returns to the same position is the circumference of the wheel, so \( C = 35 \, \text{cm} \).

Step2: Calculate the radius

Use \( C = 2\pi r \) to find \( r \):
\( r = \frac{C}{2\pi} = \frac{35}{2\pi} \approx \frac{35}{6.283} \approx 5.57 \, \text{cm} \).

Step3: Compute the area

Use \( A = \pi r^2 \):
\( A \approx \pi (5.57)^2 \approx 3.1416 \times 31.02 \approx 97.5 \, \text{cm}^2 \).

Answer:

97.5 cm²