To find the approximate radius of a sphere with the same surface area as the state of Alaska, follow these steps:
1. Understand the problem:
- We are given the surface area of Alaska, which is 663,267 square miles.
- We need to find the radius of a sphere that has an equivalent surface area.
2. Recall the formula for the surface area of a sphere:
- The surface area [tex]\( A \)[/tex] of a sphere can be calculated using the formula:
[tex]\[
A = 4 \pi r^2
\][/tex]
where [tex]\( r \)[/tex] is the radius of the sphere.
3. Rearrange the formula to solve for the radius [tex]\( r \)[/tex]:
[tex]\[
r^2 = \frac{A}{4 \pi}
\][/tex]
[tex]\[
r = \sqrt{\frac{A}{4 \pi}}
\][/tex]
4. Substitute the given surface area of Alaska into the rearranged formula:
[tex]\[
r = \sqrt{\frac{663,267}{4 \pi}}
\][/tex]
5. Calculate the radius:
- The result from the calculation (details omitted) yields a radius of approximately 229.74 miles.
6. Compare the calculated radius to the given multiple choice options:
- The choices are:
A. 54 miles
B. 117 miles
C. 230 miles
D. 52,781 miles
7. Determine the closest choice to the calculated radius:
- The calculated radius is approximately 229.74 miles, which is very close to 230 miles.
Therefore, the best answer from the choices provided is:
- C. 230 miles
