Final answer:
The area of a telescope lens with a radius of 2 feet is approximately 4 π or 12.56636 square feet, based on the formula for the area of a circle.
Step-by-step explanation:
To determine the area of the lens of a telescope given that it has a radius of 2 feet, you apply the formula for the area of a circle:
Area = π × radius2
Plugging the given radius into the formula, we get:
Area = π × (2 feet)2
Area = π × 4 square feet
Area = 4 π square feet
Since π (pi) is approximately 3.14159, you can calculate the numerical value as:
Area = 4 × 3.14159
Area = 12.56636 square feet
The lens's area is thus approximately 12.56636 square feet, which is the light-collecting area of the telescope's lens.