Question

Suppose astronomers built a 20-meter telescope. How much greater would its light-collecting area be than that of the 10-meter Keck telescope?

Answer 1

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 =$\frac{\pi d^{2}}{4}$

Where d is the diameter of the circle = 20-m

$A_{1} = \frac{\pi d^{2}}{4}$

$A_{1} = \frac{\pi (20^{2})}{4}$

A₁ = 314.2 m²

Step 2: Calculate light-collecting area of a  10-meter Keck telescope (A₂)

$A_{2} = \frac{\pi d^{2}}{4}$

Where d is the diameter of the circle = 10-m

$A_{2} = \frac{\pi (10^{2})}{4}$

A₂ = 78.55 m²

Step 3: divide A₁ by A₂  

$= \frac{314.2 m^2}{78.55 m^2}$

= 4

Therefor,  the 20-meter telescope light-collecting area would be 4 times greater than that of the 10-meter Keck telescope.