To determine the volume of a sphere with a given radius, we use the formula:
[tex]\[ V = \frac{4}{3} \pi r^3 \][/tex]
where:
- [tex]\( V \)[/tex] is the volume of the sphere,
- [tex]\( \pi \)[/tex] is a mathematical constant approximately equal to 3.14159,
- [tex]\( r \)[/tex] is the radius of the sphere.
Given that the radius [tex]\( r \)[/tex] is 25.9 inches, we substitute this value into the formula.
Step 1: Calculate [tex]\( r^3 \)[/tex]:
[tex]\[ r^3 = 25.9^3 = 17345.879 \text{ cubic inches} \][/tex]
Step 2: Multiply this result by [tex]\( \pi \)[/tex]:
[tex]\[ \pi \times 17345.879 = 54462.50 \text{ cubic inches} \][/tex]
Step 3: Finally, multiply the result by [tex]\(\frac{4}{3}\)[/tex] to obtain the volume:
[tex]\[ V = \frac{4}{3} \times 54462.50 = 72775.953 \text{ cubic inches} \][/tex]
Thus, the exact volume of the sphere is approximately [tex]\( 72775.953 \)[/tex] cubic inches.
Step 4: To round this volume to the nearest tenth, we look at the first decimal place, which is [tex]\( 0.953 \)[/tex]:
By convention, if the remainder after the decimal is 0.5 or greater, we round up.
Thus, [tex]\( 72775.953 \)[/tex] rounds to [tex]\( 72776.0 \)[/tex].
Therefore, the volume of the sphere with a radius of 25.9 inches, rounded to the nearest tenth of a cubic inch, is [tex]\( 72776.0 \)[/tex] in³.
