Question

If the measure of the arc associated with the Pacific Ocean is approximately 125°, which of the following represents the proportion of Earth's surface that is covered by the Pacific Ocean?

a) 25%
b) 30%
c) 35%
d) 40%

Answer 1

The proportion of Earth's surface covered by the Pacific Ocean is calculated as the ratio of the Pacific Ocean's arc measure to the total degrees in a circle. Applying this, 125° over 360° times 100% equals approximately 34.72%, so 35% is the closest option.

Step-by-step explanation:

To determine the proportion of Earth's surface that is covered by the Pacific Ocean, given that the measure of the arc associated with the Pacific Ocean is approximately 125°, we first consider the total number of degrees in a full circle, which is 360°. Since the Earth is a sphere, these degrees can represent the division of Earth's surface into segments based on the angle of the arc that the segment subtends at the Earth's center.

Calculating the proportion covered by the Pacific Ocean, we can set up a ratio of the arc's degrees to the total degrees in a circle:

1. Arbitrary measure of Pacific Ocean arc = 125°
2. Total degrees in a circle = 360°
3. Proportion of Earth's surface = (Pacific Ocean arc / Total degrees) x 100%
4. Proportion of Earth's surface = (125° / 360°) x 100%
5. Proportion of Earth's surface = 34.72%

Therefore, option c) 35% most closely represents the proportion of Earth's surface that is covered by the Pacific Ocean.