Question

How much greater is the light-collecting area of a 6-meter telescope than a 3-meter telescope? How much greater is the light-collecting area of a 6- telescope than a 3- telescope?
A) two times
B) four times
C) six times

Answer 1

Answer:

B) four times

Explanation:

Area of 6 meter telescope

$A_1=\pi \frac{D^2}{4}\\\Rightarrow A_1=9\pi$

Area of 3 meter telescope

$A_2=\pi \frac{D^2}{4}\\\Rightarrow A_1=2.25\pi$

Dividing the equations we get

$\frac{A_1}{A_2}=\frac{9\pi}{2.25\pi}\\\Rightarrow A_1=4A_2$

Hence, the 6-meter telescope has 4 times the light-collecting area of the 3-meter telescope.