To find the volume of a sphere with a radius of 49.5 inches, we can use the formula for the volume of a sphere:
[tex]\[ V = \frac{4}{3} \pi r^3 \][/tex]
Here, [tex]\( r = 49.5 \)[/tex] inches.
Let's walk through the calculations step-by-step:
1. Calculate [tex]\( r^3 \)[/tex] (the radius cubed):
[tex]\[ 49.5^3 = 49.5 \times 49.5 \times 49.5 \][/tex]
2. Perform the calculation:
[tex]\[
49.5 \times 49.5 = 2450.25
\][/tex]
[tex]\[
2450.25 \times 49.5 = 121202.375
\][/tex]
Therefore,
[tex]\[
49.5^3 = 121202.375
\][/tex]
3. Multiply by [tex]\(\pi\)[/tex] (pi):
[tex]\[
\pi \approx 3.141592653589793
\][/tex]
[tex]\[
\pi \times 121202.375 \approx 3.141592653589793 \times 121202.375 \approx 380554.9215
\][/tex]
4. Multiply by [tex]\(\frac{4}{3}\)[/tex]:
[tex]\[
\frac{4}{3} \times 380554.9215 \approx 4 \times 126851.6405 \approx 506206.154
\][/tex]
Rounding:
Finally, we round the result to the nearest tenth:
[tex]\[
506206.154 \approx 506206.2 \text{ cubic inches}
\][/tex]
Thus, the volume of the sphere with a radius of 49.5 inches, rounded to the nearest tenth, is approximately [tex]\(506206.2\)[/tex] cubic inches.
