Answer: A. $\dfrac{8788\pi}{375}$

Explanation:1. Understand the problem: We have a sphere with a radius of $\dfrac{13}{5}$ feet. We need to find the volume of the sphere in cubic feet.

2. Recall the formula for the volume of a sphere: The volume $V$ of a sphere with radius $r$ is given by the formula $V = \dfrac{4}{3}\pi r^3$.

3. Substitute the given radius into the formula: The radius $r = \dfrac{13}{5}$ feet. $V = \dfrac{4}{3}\pi \left(\dfrac{13}{5}\right)^3$

4. Calculate $r^3$: $\left(\dfrac{13}{5}\right)^3 = \dfrac{13^3}{5^3} = \dfrac{13 \times 13 \times 13}{5 \times 5 \times 5} = \dfrac{169 \times 13}{25 \times 5} = \dfrac{2197}{125}$

5. Substitute this back into the volume formula: $V = \dfrac{4}{3}\pi \left(\dfrac{2197}{125}\right)$

6. Multiply the fractions: $V = \dfrac{4 \times 2197}{3 \times 125}\pi$ $V = \dfrac{8788}{375}\pi$

7. Compare with the given options: [A] $\dfrac{8788\pi}{375}$ [B] $\dfrac{28\pi}{5}$ [C] $\dfrac{52\pi}{15}$ [D] $\dfrac{13\pi}{5}$ Our calculated volume $\dfrac{8788\pi}{375}$ matches option [A].

8. Conclusion: The volume of the sphere is $\dfrac{8788\pi}{375}$ cubic feet.