question 37\nhow much greater is the light - collecting area of a 10 - meter telescope than a 2 - meter…

Explanation:

Step1: Recall area formula for circle

The light - collecting area of a telescope (assumed circular) is $A = \pi r^{2}$. For a telescope with diameter $d$, $r=\frac{d}{2}$.

Step2: Calculate area of 10 - meter telescope

Let $d_1 = 10$ meters, then $r_1=\frac{10}{2}=5$ meters. So $A_1=\pi r_1^{2}=\pi\times5^{2}=25\pi$ square meters.

Step3: Calculate area of 2 - meter telescope

Let $d_2 = 2$ meters, then $r_2=\frac{2}{2}=1$ meter. So $A_2=\pi r_2^{2}=\pi\times1^{2}=\pi$ square meters.

Step4: Find the ratio of the areas

The ratio $\frac{A_1}{A_2}=\frac{25\pi}{\pi}=25$.

Answer:

D. 25 times