To calculate the volume [tex]\( V \)[/tex] of a sphere given its radius [tex]\( r \)[/tex] and the value of [tex]\( \pi \)[/tex], you can use the formula:
[tex]\[ V = \left(\frac{4}{3}\right) \pi r^3 \][/tex]
Let's go through the calculation step by step using the given values:
1. Given Information:
- Radius [tex]\( r \)[/tex] of the sphere = 6 feet
- [tex]\(\pi \)[/tex] (pi) = 3.14
2. Substitute the given radius and [tex]\(\pi \)[/tex] into the formula:
[tex]\[ V = \left(\frac{4}{3}\right) \cdot 3.14 \cdot (6)^3 \][/tex]
3. Calculate [tex]\( r^3 \)[/tex]:
[tex]\[ (6)^3 = 6 \cdot 6 \cdot 6 = 216 \][/tex]
4. Multiply by [tex]\(\pi \)[/tex]:
[tex]\[ 3.14 \cdot 216 = 678.24 \][/tex]
5. Multiply by [tex]\(\frac{4}{3}\)[/tex]:
[tex]\[ V = \left(\frac{4}{3}\right) \cdot 678.24 \][/tex]
6. Final Calculation:
[tex]\[ V = 904.32 \][/tex]
After rounding to two decimal places, the volume [tex]\( V \)[/tex] of the sphere is:
[tex]\[ V \approx 904.32 \][/tex]
Therefore, the volume of the sphere when the radius is 6 feet is approximately 904.32 cubic feet.
