Question: Find the volume of the sphere.
Either enter an exact answer in terms of $\pi$, or use
3.14 for $\pi$ and round your final answer to the
nearest hundredth if applicable.
1. **State the problem:** We need to find the volume of a sphere with radius $r = \frac{1}{2}$.
2. **Formula for the volume of a sphere:**
$$V = \frac{4}{3} \pi r^3$$
This formula calculates the volume based on the radius $r$.
3. **Substitute the radius:**
$$V = \frac{4}{3} \pi \left(\frac{1}{2}\right)^3$$
4. **Calculate the cube of the radius:**
$$\left(\frac{1}{2}\right)^3 = \frac{1^3}{2^3} = \frac{1}{8}$$
5. **Substitute back:**
$$V = \frac{4}{3} \pi \times \frac{1}{8}$$
6. **Simplify the fraction:**
$$V = \frac{4}{3} \times \frac{1}{8} \pi = \frac{4 \times 1}{3 \times 8} \pi = \frac{4}{24} \pi$$
7. **Simplify the fraction $\frac{4}{24}$:**
$$\frac{4}{24} = \frac{\cancel{4}^1}{\cancel{24}^6} = \frac{1}{6}$$
8. **Final exact volume:**
$$V = \frac{1}{6} \pi$$
9. **Approximate using $\pi \approx 3.14$:**
$$V \approx \frac{1}{6} \times 3.14 = 0.5233...$$
10. **Round to nearest hundredth:**
$$V \approx 0.52$$
**Answer:** The volume of the sphere is exactly $$\frac{1}{6} \pi$$ or approximately $0.52$ when rounded to the nearest hundredth.