1. **State the problem:** We are given the volume formula of a cone: $$V = \frac{1}{3} \pi r^2 h$$ (a) Make $r$ the subject of the formula. (b) Find the base radius $r$ of a cone with height $h = 17$ cm and volume $V = 14,732$ cm³, using $\pi r^2 = \frac{22}{7}$. 2. **Rearrange the formula to make $r$ the subject:** Starting with: $$V = \frac{1}{3} \pi r^2 h$$ Multiply both sides by 3: $$3V = \pi r^2 h$$ Divide both sides by $\pi h$: $$\frac{3V}{\pi h} = r^2$$ Take the square root of both sides: $$r = \sqrt{\frac{3V}{\pi h}}$$ 3. **Calculate $r$ using given values:** Substitute $V=14,732$ cm³, $h=17$ cm, and $\pi r^2 = \frac{22}{7}$ (note: this suggests using $\pi = \frac{22}{7}$): $$r = \sqrt{\frac{3 \times 14,732}{\frac{22}{7} \times 17}}$$ Calculate denominator: $$\frac{22}{7} \times 17 = \frac{22 \times 17}{7} = \frac{374}{7}$$ Calculate numerator: $$3 \times 14,732 = 44,196$$ So: $$r = \sqrt{\frac{44,196}{\frac{374}{7}}} = \sqrt{44,196 \times \frac{7}{374}}$$ Calculate inside the root: $$44,196 \times \frac{7}{374} = \frac{44,196 \times 7}{374} = \frac{309,372}{374} \approx 827.25$$ Take square root: $$r \approx \sqrt{827.25} \approx 28.77$$ **Final answer:** (a) $$r = \sqrt{\frac{3V}{\pi h}}$$ (b) The base radius $r$ is approximately $28.77$ cm.