Certainly! Let's solve the problem step by step.
1. Initial Diameter and Reduction:
- The initial diameter of the globe is 18 inches.
- If the dimensions of the globe are reduced by half, the new diameter will be:
[tex]\[
\text{Reduced Diameter} = \frac{18}{2} = 9 \text{ inches}
\][/tex]
2. Finding the Radius:
- The radius is half of the diameter. So, for the reduced globe:
[tex]\[
\text{Radius} = \frac{9}{2} = 4.5 \text{ inches}
\][/tex]
3. Volume of a Sphere Formula:
- The volume [tex]\( V \)[/tex] of a sphere is given by:
[tex]\[
V = \frac{4}{3} \pi r^3
\][/tex]
- Given [tex]\(\pi = 3.14\)[/tex]:
[tex]\[
V = \frac{4}{3} \times 3.14 \times (4.5)^3
\][/tex]
4. Calculating the Volume:
- First, calculate [tex]\( (4.5)^3 \)[/tex]:
[tex]\[
(4.5)^3 = 4.5 \times 4.5 \times 4.5 = 91.125
\][/tex]
- Now, plug this back into the volume formula:
[tex]\[
V = \frac{4}{3} \times 3.14 \times 91.125
= \frac{4}{3} \times 286.1325
= 4 \times 95.3775 \approx 381.51 \text{ cubic inches}
\][/tex]
5. Rounding to the Nearest Tenth:
- The calculated volume is approximately 381.51 cubic inches.
- Rounding 381.51 to the nearest tenth gives:
[tex]\[
381.5 \text{ cubic inches}
\][/tex]
Conclusion:
The volume of the reduced globe is approximately [tex]\( 381.5 \, \text{in}^3 \)[/tex].
So, the correct answer is [tex]\( 381.5 \, \text{in}^3 \)[/tex].
