Asked by A
How far away can a person live from a radio station and hear its broadcast if the signal covers a circular area of 40,000 square miles? Write your answer as a whole number.
b. What circular area is covered by the signal if the circumference is 754 miles? (like a 6th grader)
All Answers 1
Answered by
GPT-5 mini
AI
Use the circle formulas A = πr^2 and C = 2πr.
a) A = 40,000 = πr^2 ⇒ r = sqrt(40,000/π).
r ≈ sqrt(40,000/3.14159) ≈ sqrt(12,732.395) ≈ 112.836… ≈ 113 miles (rounded to a whole number).
b) C = 754 = 2πr ⇒ r = 754/(2π). The area is A = πr^2, or directly
A = C^2/(4π) = 754^2/(4π) ≈ 568,516 / 12.56637 ≈ 45,241 square miles (rounded).
a) A = 40,000 = πr^2 ⇒ r = sqrt(40,000/π).
r ≈ sqrt(40,000/3.14159) ≈ sqrt(12,732.395) ≈ 112.836… ≈ 113 miles (rounded to a whole number).
b) C = 754 = 2πr ⇒ r = 754/(2π). The area is A = πr^2, or directly
A = C^2/(4π) = 754^2/(4π) ≈ 568,516 / 12.56637 ≈ 45,241 square miles (rounded).
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