1. Problem 10: Calculate the total weight in ounces of ten cone-shaped ice cubes with radius 1.5 inches and height 2 inches, given 1 cubic inch ≈ 0.55 ounce. 2. Use the volume formula for a cone: $$V = \frac{1}{3} \pi r^2 h$$ where $r$ is radius and $h$ is height. 3. Calculate the volume of one ice cube: $$V = \frac{1}{3} \pi (1.5)^2 (2) = \frac{1}{3} \pi \times 2.25 \times 2 = \frac{1}{3} \pi \times 4.5$$ 4. Simplify: $$V = \frac{4.5}{3} \pi = 1.5 \pi \approx 1.5 \times 3.1416 = 4.7124 \text{ cubic inches}$$ 5. Calculate the weight of one ice cube: $$\text{weight} = 4.7124 \times 0.55 = 2.5918 \text{ ounces}$$ 6. Calculate the weight of ten ice cubes: $$10 \times 2.5918 = 25.918 \text{ ounces}$$ 7. Round to the nearest tenth: $$25.9 \text{ ounces}$$ --- 8. Problem 12: Find the error in Carmen's calculation of the volume of a cone-shaped vase with height 6 inches and diameter 4 inches. 9. Correct radius calculation: radius $r = \frac{\text{diameter}}{2} = \frac{4}{2} = 2$ inches. 10. Correct volume formula: $$V = \frac{1}{3} \pi r^2 h = \frac{1}{3} \pi (2)^2 (6) = \frac{1}{3} \pi \times 4 \times 6$$ 11. Simplify: $$V = \frac{1}{3} \pi \times 24 = 8 \pi \approx 8 \times 3.1416 = 25.1328 \text{ cubic inches}$$ 12. Carmen's mistake was using diameter as radius (4 instead of 2), leading to an overestimated volume. Final answers: - Problem 10: Total weight is approximately 25.9 ounces. - Problem 12: Correct volume is approximately 25.1 cubic inches, not 100.5.