Question

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

Answer 1

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:

$A=r^{2}\pi$

Where r is the radius of the circle.

2. The diameter of a circle is:

$D=\frac{r}{2}$

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:

$A_1=(\frac{50m}{2})^{2}\pi=1963,49m^{2}$

4. And the light-collecting area of a 10-meter keck telescope is:

$A_2=(\frac{10m}{2})^{2}\pi=78.53m^{2}$

5. Divide $A_1$ by $A_2$, then:

$\frac{1963.49m^{2}}{78.53m^{2}}=25$

6. Therefore, its light-collecting area would be 25 times greater than that of the 10-meter keck telescope.