Certainly! Let's walk through the solution step by step:
1. Identify the given information:
- The diameter of the spherical water tank is 14.5 feet.
- We are using π (pi) = 3.14.
2. Calculate the radius of the sphere:
- The radius (r) is half of the diameter.
- Therefore, the radius [tex]\( r \)[/tex] is [tex]\( 14.5 \, \text{feet} / 2 \)[/tex].
- That gives us [tex]\( r = 7.25 \)[/tex] feet.
3. Use the formula for the volume of a sphere:
- The formula for the volume [tex]\( V \)[/tex] of a sphere is [tex]\( V = \frac{4}{3} \pi r^3 \)[/tex].
4. Substitute the values into the formula:
- Substitute [tex]\( \pi = 3.14 \)[/tex] and [tex]\( r = 7.25 \)[/tex]:
[tex]\[
V = \frac{4}{3} \times 3.14 \times (7.25)^3
\][/tex]
5. Calculate the volume:
- First, compute the cube of the radius:
[tex]\[
(7.25)^3 = 7.25 \times 7.25 \times 7.25
\][/tex]
- Then, multiply by π and [tex]\( \frac{4}{3} \)[/tex]:
[tex]\[
V = \frac{4}{3} \times 3.14 \times 381.078125
\][/tex]
- Simplify the multiplication:
[tex]\[
V = \frac{4}{3} \times 1196.58625
\][/tex]
- Multiply by [tex]\( \frac{4}{3} \)[/tex]:
[tex]\[
V = 1595.4470833333332 \, \text{cubic feet}
\][/tex]
Therefore, the spherical water tank can hold approximately 1595.447 cubic feet of water.
