To find the volume of a sphere, we use the formula:
\(\[ V = \frac{4}{3} \pi r^3 \]\)
where \(\( V \)\) is the volume and \(\( r \)\) is the radius of the sphere.
Given that the diameter of the sphere is 12 ft, we first need to find the radius. The radius \(\( r \)\) is half of the diameter:
\(\[ r = \frac{\text{diameter}}{2} \]\)
\(\[ r = \frac{12 \text{ ft}}{2} \]\)
\(\[ r = 6 \text{ ft} \]\)
Now we substitute the radius back into the volume formula:
\(\[ V = \frac{4}{3} \pi (6 \text{ ft})^3 \]\)
Next, we need to calculate \(\( (6 \text{ ft})^3 \)\):
\(\[ (6 \text{ ft})^3 = 6 \text{ ft} \times 6 \text{ ft} \times 6 \text{ ft} = 216 \text{ ft}^3 \]\)
Now we substitute \(\( 216 \text{ ft}^3 \)\) into the volume formula:
\(\[ V = \frac{4}{3} \pi (216 \text{ ft}^3) \]\)
Simplifying further:
\(\[ V = \frac{4}{3} \pi \times 216 \text{ ft}^3 \]\)
\(\[ V = \frac{4 \times 216 \pi}{3} \text{ ft}^3 \]\)
\(\[ V = \frac{864 \pi}{3} \text{ ft}^3 \]\)
\(\[ V = 288 \pi \text{ ft}^3 \]\)
Thus, the exact volume of the sphere is:
\(\[ 288 \pi \text{ ft}^3 \]\)
