Final answer:
To determine how much farther an asteroid travels when its orbit radius increases by 5 miles, calculate the change in the circular orbit's circumference. The additional distance traveled is 10π miles, making the correct answer (b) 10π miles.
Step-by-step explanation:
The question is asking how much farther an asteroid will travel in its orbit around planet Zeno if the radius of the orbit is increased by 5 miles. We start by acknowledging that the asteroid's path is circular. The circumference of a circle is given by the formula C = 2πr, where π is Pi (approximately 3.14159) and r is the radius of the circle.
To find out how much farther the asteroid will travel, we calculate the difference in the circumferences before and after the orbit radius increases:
C1 = 2πr (initial circumference)
C2 = 2π(r + 5) (new circumference with increased radius)
Difference = C2 - C1 = 2π(r + 5) - 2πr = 2πr + 10π - 2πr = 10π
Therefore, when the orbit radius is increased by 5 miles, the asteroid will travel 10π miles farther in one complete orbit. The correct answer to the question is (b) 10π miles.