Suppose astronomers built a 50-meter telescope. how much greater would its light-collecting area be than that of the 10-meter keck telescope?

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 r is the radius of the circle.

2. The diameter of a circle is:

Where r 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.

the answer to the expression is 83