Estimate the number of steps you would have to take to walk a distance equal to the circumference...

Question:

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 x 10{eq}^6 {/eq} m.)

Conversion Factors

Quantities are measured in specific units, for example length is measured in units of meters, miles, feet or etc. Each unit of measurement is scaled differently, a length of one meter is longer than a length of a millimeter. A conversion factor is used to convert one unit of measurement to another.

Answer and Explanation:


To calculate the number of steps required to walk a distance equal to the circumference of the Earth, we need to divide the circumference of the Earth with the length of an step. To calculate the circumference of the Earth, we use the formula for the circumference of a circle. Here we assume that the Earth is a perfect sphere.

{eq}C = 2 \pi r {/eq}

Earth's radius is {eq}r = 6.38 \times 10^6\ m {/eq}


{eq}\begin{align*} C &= 2 \pi r \\ &= 2 \pi (6.38 \times 10^6\ m) \\ &= 4.009 \times 10^7\ m \end{align*} {/eq}


To calculate the number of steps is equal to this length, we divide this with the length of a step which is 0.5 m.

{eq}\displaystyle 4.009 \times 10^7\ m \times \bigg( \frac{1\ \text{step}}{0.5\ m} \bigg) = \boxed{ 8.018 \times 10^7\ \text{ steps}} {/eq}


Therefore it takes approximately {eq}\boxed{ 8.018 \times 10^7\ \text{ steps}} {/eq} to walk a distance equal to Earth's circumference.


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Common Unit Conversions

from Business 110: Business Math

Chapter 1 / Lesson 10
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