1. **Stating the problem:** (a) Choose the correct formula for the volume of a sphere with radius $r$. (b) Given the volume of a soccer ball is $288\pi$ cm$^3$, find its radius. 2. **Formula for volume of a sphere:** The volume $V$ of a sphere with radius $r$ is given by: $$V = \frac{4}{3} \pi r^3$$ This formula is derived from integral calculus and is a standard geometric formula. 3. **Answer for part (a):** Among the options: - A: $\frac{4}{3} \pi r^3$ (correct) - B: None of the above - C: $\frac{2}{3} \pi r^3$ (incorrect) - D: $\frac{4}{3} \pi d^3$ (incorrect, $d$ is diameter, not radius) So, the correct option is **A**. 4. **Solving part (b):** Given volume $V = 288\pi$ cm$^3$, use the formula: $$288\pi = \frac{4}{3} \pi r^3$$ Divide both sides by $\pi$: $$288 = \frac{4}{3} r^3$$ Multiply both sides by $\frac{3}{4}$: $$288 \times \frac{3}{4} = r^3$$ Show cancellation: $$288 \times \cancel{\frac{3}{4}} = r^3 \quad \Rightarrow \quad 288 \times \frac{3}{4} = r^3$$ Calculate: $$288 \times \frac{3}{4} = 288 \times 0.75 = 216$$ So, $$r^3 = 216$$ Take the cube root of both sides: $$r = \sqrt[3]{216} = 6$$ 5. **Final answer:** - (a) Correct formula is $\frac{4}{3} \pi r^3$ (Option A). - (b) Radius of the soccer ball is $6$ cm.