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

B) four times

Step-by-step explanation:

Area of 6 meter telescope

`A_1=\pi (D^2)/(4)\\\Rightarrow A_1=9\pi`

Area of 3 meter telescope

`A_2=\pi (D^2)/(4)\\\Rightarrow A_1=2.25\pi`

Dividing the equations we get

`(A_1)/(A_2)=(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.