Answer:
4 times greater
Explanation:
Step 1: Calculate light-collecting area of a 20-meter telescope (A₁) by using area of a circle.
Area of circle = π*r² =[tex]\frac{\pi d^{2}}{4}[/tex]
Where d is the diameter of the circle = 20-m
[tex]A_{1} = \frac{\pi d^{2}}{4}[/tex]
[tex]A_{1} = \frac{\pi (20^{2})}{4}[/tex]
A₁ = 314.2 m²
Step 2: Calculate light-collecting area of a 10-meter Keck telescope (A₂)
[tex]A_{2} = \frac{\pi d^{2}}{4}[/tex]
Where d is the diameter of the circle = 10-m
[tex]A_{2} = \frac{\pi (10^{2})}{4}[/tex]
A₂ = 78.55 m²
Step 3: divide A₁ by A₂
[tex]= \frac{314.2 m^2}{78.55 m^2}[/tex]
= 4
Therefor, the 20-meter telescope light-collecting area would be 4 times greater than that of the 10-meter Keck telescope.
