Question

1. -/1 points estimate the number of steps you would have to take to walk a distance equal to the circumference of the earth. (we estimate that the length of a step for an average person is about 18 inches, or roughly 0.5 m. the radius of the earth is 6.38 × 10⁶ m.) options: 10⁵ steps, 10⁸ steps, 10¹¹ steps, 10¹⁵ steps, 10²⁰ steps

Explanation:

Step1: Calculate Earth's circumference

The formula for the circumference of a circle is \( C = 2\pi r \). Given \( r = 6.38\times 10^{6}\space m \), so \( C = 2\times\pi\times6.38\times 10^{6}\space m \approx 4.01\times 10^{7}\space m \).

Step2: Calculate number of steps

The length of one step is about \( 0.5\space m \). Let the number of steps be \( n \), then \( n=\frac{C}{\text{step length}}=\frac{4.01\times 10^{7}\space m}{0.5\space m/step}\approx 8\times 10^{7}\space steps\approx 10^{8}\space steps \) (when rounded to the nearest power of 10).

Answer:

\( 10^{8}\) steps (corresponding to the option "10⁸ steps")