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