1. **State the problem:** We have a cylinder of sherbet with height 32 cm and diameter 20 cm (radius 10 cm). The sherbet is poured into 250 conical containers each with diameter 5 cm (radius 2.5 cm) and unknown depth $d$ cm. We need to find $d$. 2. **Formulas:** - Volume of cylinder: $$V_{cyl} = \pi r^2 h$$ - Volume of cone: $$V_{cone} = \frac{1}{3} \pi r^2 d$$ 3. **Calculate volume of the cylinder:** $$V_{cyl} = \pi \times 10^2 \times 32 = 3200\pi$$ 4. **Total volume of 250 cones equals volume of cylinder:** $$250 \times V_{cone} = V_{cyl}$$ $$250 \times \frac{1}{3} \pi \times 2.5^2 \times d = 3200\pi$$ 5. **Simplify and solve for $d$:** $$250 \times \frac{1}{3} \pi \times 6.25 \times d = 3200\pi$$ $$\frac{250 \times 6.25}{3} \pi d = 3200\pi$$ 6. **Cancel $\pi$ from both sides:** $$\cancel{\pi} \times \frac{250 \times 6.25}{3} d = 3200 \cancel{\pi}$$ 7. **Calculate coefficient:** $$\frac{250 \times 6.25}{3} = \frac{1562.5}{3} = 520.8333...$$ 8. **Solve for $d$:** $$520.8333 d = 3200$$ $$d = \frac{3200}{520.8333} \approx 6.146$$ **Final answer:** The depth $d$ of the sherbet cone is approximately **6.15 cm**.