What is the volume of a sphere with a radius of 9 units?A.972 units3B.243 units3C.486 units3D.324 units3

1. Break Down the Problem

To find the volume of a sphere, we need to use the formula for the volume of a sphere, which is given by:

$V = \frac{4}{3} \pi r^3$

where $V$ is the volume and $r$ is the radius.

2. Relevant Concepts

1. Identify the radius: Here, $r = 9$ units.
2. Apply the volume formula for a sphere.

3. Analysis and Detail

1. Substitute the radius into the formula: $V = \frac{4}{3} \pi (9)^3$
2. Calculate $9^3$: $9^3 = 729$
3. Substitute back into the volume formula: $V = \frac{4}{3} \pi (729)$
4. Calculate: $V = \frac{4 \times 729}{3} \pi = 972 \pi$

4. Verify and Summarize

Now we approximate $\pi$ as $3.14$ for calculation: $972 \pi \approx 972 \times 3.14 \approx 3040.08 \text{ units}^3$ However, the exact volume in terms of $\pi$ is $972 \pi$ units³.

Final Answer

The volume of the sphere is approximately $3040.08$ units³, which corresponds to none of the provided options. However, if considering the volume without numerical approximation involving $\pi$, the result is $972 \pi$ units³. Therefore, it appears none of the provided options A, B, C, or D are correct in this context.