A satellite is currently in a circular orbit with radius 32,714km
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29 Mar 2024, 01:01
A satellite is currently in a circular orbit with radius 32,714 km about the center of the earth.
Select for 0.5 km the increase, to the nearest whole kilometer, in the distance the satellite travels about the center of the earth during each revolution if the orbital radius of the satellite is increased by 0.5 km. And select for 1.5 km the increase, to the nearest whole kilometer, in the distance the satellite travels about the center of the earth during each revolution if the orbital radius of the satellite is increased by 1.5 km. Make only two selections, one in each column.
According to GMAC, Geometry does not appear on the Focus Edition, but questions, such as this one, on the official practice tests indicate that knowing some basic Geometry concepts that can be considered common knowledge is necessary for getting some Quant questions correct.
Among those concepts are the Pythagorean theorem and formulas for calculating the areas of basic shapes including rectangles, triangles, and circles.
Now, this question requires use of the formula for the circumference of a circle, which is \(C = 2πr = πd\). where \(C\) is the circumference, \(r\) is the radius, \(d\) is the diameter of the circle, and the value of \(π\) is approximately \(3.14\).
Given that formula, we can see that, any time we increase the radius of a circle, we increase the circumference of the circle by \(2π\) times the increase in the radius, or by about \(6.28\) times the increase in the radius.
So, to calculate the increase in the distance the satellite travels during each revolution, we can ignore the figure 32,714 and just multiply each increase in the radius by 6.28.
If the radius is increased by 0.5 km, the distance is increased by approximately 0.5 × 6.28 = 3.14, which rounded to the nearest whole kilometer is 3.
If the radius is increased by 1.5 km, the distance is increased by approximately 1.5 × 6.28 = 9.42, which rounded to the nearest whole kilometer is 9.
3km
9km
27km
81km
150km
450km
Correct answer: 3km, 9km