Sphere Volume Step-by-Step Examples: Solved Textbook Problems

Example 1: Radius Given Directly (r = 6 cm)

1. Formula: = ⁴⁄₃ imes \pi imes r^3$.
2. Cube radius: $6^3 = 6 imes 6 imes 6 = 216$.
3. Multiply by 4/3: imes 216 = 288$.
4. Exact Volume: $288\pi ext{ cm}^3$.
5. Decimal Volume: $288 imes 3.14159265 \approx 904.78 ext{ cm}^3$.

Example 2: Diameter Given (d = 14 m)

1. Find radius: = 14 / 2 = 7 ext{ m}$.
2. Cube radius: $7^3 = 343$.
3. Multiply by 4/3: imes 343 = 457.33$.
4. Exact Volume: $457.33\pi ext{ m}^3$ or $rac{1372\pi}{3} ext{ m}^3$.
5. Decimal Volume: $\approx 1,436.76 ext{ m}^3$.