1. **State the problem:** We have a metal block with mass 68.7 kg. Each cubic centimeter (cm³) of this metal has a mass of 8.1 g. The block is melted and recast into cylinders with length 7.4 cm and diameter 2.6 cm. We need to find how many complete cylinders can be made. 2. **Convert units:** Since the block mass is in kilograms and density is in grams per cm³, convert the block mass to grams: $$68.7\ \text{kg} = 68.7 \times 1000 = 68700\ \text{g}$$ 3. **Find the volume of the metal block:** Using the density formula: $$\text{Density} = \frac{\text{Mass}}{\text{Volume}} \implies \text{Volume} = \frac{\text{Mass}}{\text{Density}}$$ Given density = 8.1 g/cm³, mass = 68700 g, $$\text{Volume} = \frac{68700}{8.1} = 8481.48\ \text{cm}^3$$ 4. **Calculate the volume of one cylinder:** The volume of a cylinder is: $$V = \pi r^2 h$$ Diameter = 2.6 cm, so radius $r = \frac{2.6}{2} = 1.3$ cm, height $h = 7.4$ cm. Calculate volume: $$V = \pi \times (1.3)^2 \times 7.4 = \pi \times 1.69 \times 7.4 = \pi \times 12.506 = 39.29\ \text{cm}^3$$ 5. **Find the number of complete cylinders:** Divide the total volume of metal by the volume of one cylinder: $$\text{Number of cylinders} = \left\lfloor \frac{8481.48}{39.29} \right\rfloor = \left\lfloor 215.9 \right\rfloor = 215$$ **Final answer:** 215 complete cylinders can be made.