anonymous
  • anonymous
Find the length of the diameter of a sphere with a surface area of 490.87 km2. A. 12.5 km B. 25 km C. 6.25 km D. 3.125 km
Mathematics
schrodinger
  • schrodinger
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TuringTest
  • TuringTest
\[A=4\pi r^2\]\[d=2r\]
anonymous
  • anonymous
D
anonymous
  • anonymous
Using @Turing's formulas we have A = 4(pi)d^2 Then substituting in the known values we have 490.87/pi = d^2 Taking the square root d = 12.50 The answer is A

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anonymous
  • anonymous
Did it again and i still have D
anonymous
  • anonymous
Turing's formula's are right, and meverett's working correct. Here's another approach: \[\Large \begin{array}{l} A = 4\pi {r^2}\\ d = 2r\\ r = \frac{d}{2}\\ A = 4\pi {\left( {\frac{d}{2}} \right)^2}\\ {\left( {\frac{d}{2}} \right)^2} = \frac{A}{{4\pi }}\\ \frac{d}{2} = \sqrt {\frac{A}{{4\pi }}} \\ d = 2\sqrt {\frac{A}{{4\pi }}} \\ d = 2\sqrt {\frac{{{\rm{49}}0.{\rm{87}}}}{{4\pi }}} \\ = 12.499951\\ = 12.5 \end{array}\] Which is A.

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