Question: Find the volume
of the sphere.
V = [?]\pi cm^3
Leave your answer in terms of \pi.
V = \frac{4}{3}\pi r^3
Graph shape: A sphere is shown on the left with a dashed horizontal great-circle ellipse and a dashed diameter/radius line labeled 18 cm; position_hint = center.
1. **State the problem:** We need to find the volume $V$ of a sphere given the diameter is $18$ cm.
2. **Recall the formula for the volume of a sphere:**
$$V = \frac{4}{3} \pi r^3$$
where $r$ is the radius of the sphere.
3. **Find the radius:**
The diameter $d$ is $18$ cm, so the radius $r$ is half of the diameter:
$$r = \frac{d}{2} = \frac{18}{2} = 9 \text{ cm}$$
4. **Substitute the radius into the volume formula:**
$$V = \frac{4}{3} \pi (9)^3$$
5. **Calculate the cube of the radius:**
$$9^3 = 9 \times 9 \times 9 = 729$$
6. **Substitute and simplify:**
$$V = \frac{4}{3} \pi \times 729$$
7. **Multiply numerator and denominator to simplify:**
$$V = \frac{4 \times 729}{3} \pi = \frac{2916}{3} \pi$$
8. **Simplify the fraction:**
$$V = 972 \pi$$
**Final answer:**
$$\boxed{972 \pi \text{ cm}^3}$$