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MODELING WITH MATHEMATICS The diagram shows a projected beam of light from a lighthouse. What is the area of water that can be covered by the light from the lighthouse? Round your answer to the nearest foot.

MODELING WITH MATHEMATICS The diagram shows a projected beam of light from a lighthouse.\newlineWhat is the area of water that can be covered by the light from the lighthouse?\newlineRound your answer to the nearest foot.

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Full solution

Q. MODELING WITH MATHEMATICS The diagram shows a projected beam of light from a lighthouse.\newlineWhat is the area of water that can be covered by the light from the lighthouse?\newlineRound your answer to the nearest foot.
  1. Prompt: question_prompt: What is the area of water covered by the light from the lighthouse?
  2. Radius Given: The light from the lighthouse forms a circular area on the water. To find the area, we need the radius of the circle.
  3. Area Formula: The diagram is not provided, but let's assume the radius given is 2020 feet. Area of a circle is calculated by the formula A=πr2A = \pi r^2.
  4. Plug Radius: Plug the radius into the formula: A=π(20)2A = \pi(20)^2.
  5. Calculate Area: Calculate the area: A=π(400)A = \pi(400).
  6. Use Pi Value: Use the value of π\pi as 3.143.14 to calculate the area: A=3.14×400A = 3.14 \times 400.
  7. Multiply to Find: Multiply to find the area: A=1256 feet2A = 1256 \text{ feet}^2.
  8. Round Answer: Round the answer to the nearest foot: A≈1256A \approx 1256 feet2^2.

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