1. **Problem statement:** Calculate the total surface area of a solid cylinder with radius $3$ m and volume $72\pi$ m³. 2. **Given:** - Radius $r = 3$ m - Volume $V = 72\pi$ m³ 3. **Formula for volume of cylinder:** $$V = \pi r^2 h$$ 4. **Calculate height $h$:** $$72\pi = \pi \times 3^2 \times h$$ $$72\pi = 9\pi h$$ Divide both sides by $9\pi$: $$\frac{72\cancel{\pi}}{9\cancel{\pi}} = \cancel{9\pi} h / \cancel{9\pi}$$ $$8 = h$$ 5. **Formula for total surface area (TSA) of cylinder:** $$\text{TSA} = 2\pi r h + 2\pi r^2$$ 6. **Calculate TSA:** $$= 2\pi \times 3 \times 8 + 2\pi \times 3^2$$ $$= 48\pi + 18\pi$$ $$= 66\pi$$ 7. **Final answer:** Total surface area $= 66\pi$ m² 8. **Rounded to 3 significant figures:** $$66\pi \approx 207$$ m²