Let's solve this problem step by step:
1. Identify the original diameter of the globe:
The original diameter of the globe is 20 inches.
2. Calculate the radius of the original globe:
The radius is half of the diameter. Therefore, the radius [tex]\( r \)[/tex] is:
[tex]\[
r = \frac{20}{2} = 10 \text{ inches}
\][/tex]
3. Recall the formula for the volume of a sphere:
The volume [tex]\( V \)[/tex] of a sphere is given by the formula:
[tex]\[
V = \frac{4}{3} \pi r^3
\][/tex]
Here, [tex]\( \pi \)[/tex] is approximately 3.14, and [tex]\( r \)[/tex] is the radius.
4. Substitute the radius and [tex]\( \pi \)[/tex] into the formula to find the volume of the original globe:
[tex]\[
V = \frac{4}{3} \times 3.14 \times (10)^3
\][/tex]
[tex]\[
V = \frac{4}{3} \times 3.14 \times 1000
\][/tex]
[tex]\[
V = \frac{4}{3} \times 3140
\][/tex]
[tex]\[
V = 4186.666666666667 \text{ cubic inches}
\][/tex]
5. Round the volume to the nearest tenth:
The given volume [tex]\( 4186.666666666667 \)[/tex] rounds to [tex]\( 4186.7 \)[/tex].
6. Compare the calculated volume with the provided choices:
The calculated volume is approximately [tex]\( 4186.7 \)[/tex] cubic inches. Among the given options (166.7, 1333.3, 5.233, 41857), none of them match exactly, but the closest correct option here is likely:
[tex]\[ \boxed{4186.7} \][/tex]
Given that the exact volume computed does not perfectly fit any of the choices provided, the answer corresponding to the actual calculation should have been [tex]\( 4186.7 \)[/tex] cubic inches if considered independently. Since the closest match is 41857, either there's some error or further context required. But with the true computation:
[tex]\[ \boxed{4186.7} \][/tex] cubic inches would be the correct volume rounding to the nearest tenth (ignoring discrepancies).
