How much greater is the light-collecting area of one of the 10-meter keck telescopes than that of the 5-meter hale telescope?

The light-collecting area of the 10-meter Keck telescope is 4 times greater than the light-collecting area of the 5-meter Hale telescope.

Why?

We can calculate the light-collecting area of a telescope by using its diameter/radius.  To do that, we can use the following formula:

Now, to know how much greater is the collecting area of the 10-meter keck telescope compared to the collecting area of the 5-meter hale telescope, we need to calculate their light-collecting areas and compare them.

For the 10-meter keck telescope, we have:

For the 5-meter hale telescope, we have:

Now, comparing the areas, we have:

Hence, we have that the light-collecting area of the 10-meter keck telescope is 4 times greater than the light-collecting area of the 5-meter hale telescope.

Have a nice day!

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