Question

How much greater is the light-collecting area of a 6-metermeter telescope than a 3-metermeter telescope?

Answer 1

Light collecting area of 6 mm telescope is 4 times greater than light collecting area of 3 mm telescope.

Step-by-step explanation:

Diameter of 1st telescope = 6 mm

Diameter of 2nd telescope = 3 mm

Light collecting area of telescope is given as

`A=(\pi D^(2))/(4)`

For 1st telescope

`A_(1)=(\pi (6)^(2))/(4)\\\\A_(1)=9\pi`

For 2nd telescope

`A_(2)=(\pi (3)^(2))/(4)\\\\A_(1)=(9)/(4)\pi`

`A_(1)=(1)/(4)A_(2)\\\\A_(2)=4A_(1)`

Which means light collecting area of 6 mm telescope is 4 times greater than light collecting area of 3 mm telescope.