Question

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

Answer 1

\[A=4\pi r^2\]\[d=2r\]

Answer 2

D

Answer 3

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

Answer 4

Did it again and i still have D

Answer 5

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.