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Answer: Its light-collecting area would be 25 times greater than that of the 10-meter keck telescope.
Step-by-step explanation:
1. To solve this problem you must apply the formula for calculate the area of a circle, which is shown below:
Where<em> r</em> is the radius of the circle.
2. The diameter of a circle is:
Where <em>r</em> is the radius of the circle.
3. Therefore, keeping this on mind, you have that the light-collecting area of a 50-meter keck telescope is:
4. And the light-collecting area of a 10-meter keck telescope is:
5. Divide by
, then:
6. Therefore, its light-collecting area would be 25 times greater than that of the 10-meter keck telescope.