How do you calculate the surface area of a sphere if its circumference is 40 feet, rounding the result to the nearest tenth?

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To calculate the surface area of a sphere when given its circumference, you can follow these steps:

  1. Understand the relationship between circumference and radius: The formula for the circumference (C) of a sphere is given by:
  2. C = 2πr
  3. Where r is the radius of the sphere and π (pi) is approximately 3.14159.
  4. Calculate the radius: Rearranging the circumference formula helps us find the radius:
  5. r = C / (2π)
  6. By substituting the given circumference of 40 feet into the formula:
  7. r = 40 / (2 * π) ≈ 40 / 6.28318 ≈ 6.366
  8. So, the radius (r) of the sphere is approximately 6.366 feet.

Next, calculate the surface area: The formula for the surface area (A) of a sphere is:

  • A = 4πr²

Now, we can substitute the radius into the surface area formula:

  • A = 4π(6.366)²
  • A = 4π(40.5098) ≈ 4(3.14159)(40.5098) ≈ 509.9047

After calculating, the surface area of the sphere is approximately 509.9 square feet when rounded to the nearest tenth.

Final answer: The surface area of the sphere with a circumference of 40 feet is approximately 509.9 square feet.

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