1. **Problem statement:** Find the volume of water in the cylinder with a metal ball bearing fully submerged inside it. 2. **Given:** - Height of water in cylinder, $h = 30$ cm - Diameter of metal ball bearing, $d = 2$ cm, so radius $r_b = \frac{2}{2} = 1$ cm - Diameter of cylinder base, $d_c = 15$ cm, so radius $r_c = \frac{15}{2} = 7.5$ cm 3. **Formula for volume of a cylinder:** $$V = \pi r^2 h$$ 4. **Formula for volume of a sphere:** $$V = \frac{4}{3} \pi r^3$$ 5. **Calculate volume of water if no ball bearing:** $$V_{water+ball} = \pi (7.5)^2 (30) = \pi \times 56.25 \times 30 = 1687.5\pi$$ 6. **Calculate volume of metal ball bearing:** $$V_{ball} = \frac{4}{3} \pi (1)^3 = \frac{4}{3} \pi = 1.3333\pi$$ 7. **Volume of water only (subtract ball volume):** $$V_{water} = V_{water+ball} - V_{ball} = 1687.5\pi - 1.3333\pi = (1687.5 - 1.3333)\pi = 1686.1667\pi$$ 8. **Calculate numerical value:** $$V_{water} \approx 1686.1667 \times 3.1416 = 5295.5 \text{ cm}^3$$ **Final answer:** The volume of water in the cylinder is approximately **5296 cm³** (rounded to nearest whole number).