1. **Problem Statement:** Find the volume of water left in a right circular cylinder of radius 60 cm and height 180 cm after placing a solid consisting of a right circular cone of height 120 cm and radius 60 cm standing on a hemisphere of radius 60 cm inside it. 2. **Formulas and Important Rules:** - Volume of a cylinder: $$V_{cyl} = \pi r^2 h$$ - Volume of a cone: $$V_{cone} = \frac{1}{3} \pi r^2 h$$ - Volume of a hemisphere: $$V_{hemi} = \frac{2}{3} \pi r^3$$ 3. **Calculate the volume of the cylinder:** Given radius $$r = 60$$ cm and height $$h = 180$$ cm, $$V_{cyl} = \pi \times 60^2 \times 180 = \pi \times 3600 \times 180 = 648000\pi \text{ cm}^3$$ 4. **Calculate the volume of the cone:** Given radius $$r = 60$$ cm and height $$h = 120$$ cm, $$V_{cone} = \frac{1}{3} \pi \times 60^2 \times 120 = \frac{1}{3} \pi \times 3600 \times 120 = 144000\pi \text{ cm}^3$$ 5. **Calculate the volume of the hemisphere:** Given radius $$r = 60$$ cm, $$V_{hemi} = \frac{2}{3} \pi \times 60^3 = \frac{2}{3} \pi \times 216000 = 144000\pi \text{ cm}^3$$ 6. **Calculate the total volume of the solid (cone + hemisphere):** $$V_{solid} = V_{cone} + V_{hemi} = 144000\pi + 144000\pi = 288000\pi \text{ cm}^3$$ 7. **Calculate the volume of water left in the cylinder:** $$V_{water} = V_{cyl} - V_{solid} = 648000\pi - 288000\pi = 360000\pi \text{ cm}^3$$ 8. **Final answer:** The volume of water left in the cylinder is $$360000\pi \approx 1130973.24 \text{ cm}^3$$.