Question

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

Answer 1

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:

`CollectingArea=\pi*((diameter)/(2))^(2) =  \pi radius^(2)`

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:

`Keck=\pi *((10m)/(2))^(2)=\pi *(5m)^(2)=25\pi m^(2)`

For the 5-meter hale telescope, we have:

`Keck=\pi *((5m)/(2))^(2)=\pi *(2.5m)^(2)=6.25\pi m^(2)`

Now, comparing the areas, we have:

`Ratio=(KecksArea)/(HalesArea)=(25\pi m^(2) )/(6.25\pi m^(2))=4`

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!