1. **State the problem:** We have five figures: Cylinder #1 (height 5 in, radius 6 in), Cone #1 (height 5 in, radius 6 in), Cylinder #2 (height 15 in, radius 6 in), Cone #2 (height 15 in, radius 6 in), and a Sphere (radius 6 in). Part A: Identify which figures have volume greater than 600 cubic inches. Part B: Find how many times greater the volume of the Sphere is compared to Cone #1, rounded to the nearest tenth. 2. **Formulas for volumes:** - Cylinder volume: $$V=\pi r^2 h$$ - Cone volume: $$V=\frac{1}{3}\pi r^2 h$$ - Sphere volume: $$V=\frac{4}{3}\pi r^3$$ 3. **Calculate volumes:** - Cylinder #1: $$V=\pi \times 6^2 \times 5=\pi \times 36 \times 5=180\pi \approx 565.49$$ cubic inches - Cone #1: $$V=\frac{1}{3}\pi \times 6^2 \times 5=\frac{1}{3}\pi \times 36 \times 5=60\pi \approx 188.50$$ cubic inches - Cylinder #2: $$V=\pi \times 6^2 \times 15=\pi \times 36 \times 15=540\pi \approx 1696.46$$ cubic inches - Cone #2: $$V=\frac{1}{3}\pi \times 6^2 \times 15=\frac{1}{3}\pi \times 36 \times 15=180\pi \approx 565.49$$ cubic inches - Sphere: $$V=\frac{4}{3}\pi \times 6^3=\frac{4}{3}\pi \times 216=288\pi \approx 904.78$$ cubic inches 4. **Compare volumes to 600:** - Cylinder #1: 565.49 < 600 (No) - Cone #1: 188.50 < 600 (No) - Cylinder #2: 1696.46 > 600 (Yes) - Cone #2: 565.49 < 600 (No) - Sphere: 904.78 > 600 (Yes) 5. **Answer Part A:** Figures with volume greater than 600 cubic inches are Cylinder #2 and Sphere. 6. **Answer Part B:** Calculate how many times greater the Sphere's volume is than Cone #1: $$\frac{904.78}{188.50} \approx 4.8$$ **Final answers:** - Part A: Cylinder #2 and Sphere - Part B: Sphere's volume is approximately 4.8 times greater than Cone #1's volume.