The light gathering power of a telescope is proportional to the area of its aperture (the diameter of its main lens or mirror). The area (A) of a circle is given by the formula A = πr², where r is the radius of the circle. In this case, the radius is half of the diameter of the telescope's aperture.

1. First, calculate the area of the 10 Meter Keck Telescope:
The radius of the 10 Meter Keck Telescope is 10/2 = 5 meters.
So, its area is A = π(5m)² = 78.54 square meters.

2. Next, calculate the area of the 30 Meter Telescope:
The radius of the 30 Meter Telescope is 30/2 = 15 meters.
So, its area is A = π(15m)² = 706.86 square meters.

3. Finally, calculate how much more light gathering power the 30 Meter Telescope has over the 10 Meter Keck Telescope:
The difference in light gathering power is 706.86 square meters - 78.54 square meters = 628.32 square meters.

So, the 30 Meter Telescope has 628.32 square meters more light gathering power than the 10 Meter Keck Telescope.

Question

The light gathering power of a telescope is proportional to the area of its aperture (the diameter of its main lens or mirror). The area (A) of a circle is given by the formula A = πr², where r is the radius of the circle. In this case, the radius is half of the diameter of the telescope's aperture.

1. First, calculate the area of the 10 Meter Keck Telescope:
   The radius of the 10 Meter Keck Telescope is 10/2 = 5 meters.
   So, its area is A = π(5m)² = 78.54 square meters.

2. Next, calculate the area of the 30 Meter Telescope:
   The radius of the 30 Meter Telescope is 30/2 = 15 meters.
   So, its area is A = π(15m)² = 706.86 square meters.

3. Finally, calculate how much more light gathering power the 30 Meter Telescope has over the 10 Meter Keck Telescope:
   The difference in light gathering power is 706.86 square meters - 78.54 square meters = 628.32 square meters.

So, the 30 Meter Telescope has 628.32 square meters more light gathering power than the 10 Meter Keck Telescope.

Knowee AI · Accepted Answer

The light gathering power of a telescope is proportional to the area of its aperture (the diameter of its main lens or mirror). The area (A) of a circle is given by the formula A = πr², where r is the radius of the circle. In this case, the radius is half of the diameter of the telescope's aperture.

1. First, calculate the area of the 10 Meter Keck Telescope:
   The radius of the 10 Meter Keck Telescope is 10/2 = 5 meters.
   So, its area is A = π(5m)² = 78.54 square meters.

2. Next, calculate the area of the 30 Meter Telescope:
   The radius of the 30 Meter Telescope is 30/2 = 15 meters.
   So, its area is A = π(15m)² = 706.86 square meters.

3. Finally, calculate how much more light gathering power the 30 Meter Telescope has over the 10 Meter Keck Telescope:
   The difference in light gathering power is 706.86 square meters - 78.54 square meters = 628.32 square meters.

So, the 30 Meter Telescope has 628.32 square meters more light gathering power than the 10 Meter Keck Telescope.

How much more light gathering power does the 30 Meter Telescope have over the 10 Meter Keck Telescope? x

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