1. **Problem statement:** Calculate the volume of the part of the cone that is not in contact with water when a conical solid of radius 14 cm is fitted into a cylindrical tin of radius 7 cm containing water to a height of 19 cm. The cone is inserted to a depth of 18 cm. 2. **Given data:** - Cylinder radius $r_c = 7$ cm - Water height in cylinder $h_w = 19$ cm - Cone radius $r_{cone} = 14$ cm - Cone depth inside cylinder $h_{cone} = 18$ cm - Use $\pi = \frac{22}{7}$ 3. **Step 1: Calculate the volume of water in the cylinder** The volume of water in the cylinder is given by the formula for the volume of a cylinder: $$V_{water} = \pi r_c^2 h_w$$ Substitute values: $$V_{water} = \frac{22}{7} \times 7^2 \times 19 = \frac{22}{7} \times 49 \times 19$$ Calculate: $$V_{water} = 22 \times 7 \times 19 = 22 \times 133 = 2926 \text{ cm}^3$$ 4. **Step 2: Calculate the volume of the cone inside the cylinder** The volume of a cone is: $$V_{cone} = \frac{1}{3} \pi r^2 h$$ Here, the cone radius is 14 cm and height inside the cylinder is 18 cm: $$V_{cone} = \frac{1}{3} \times \frac{22}{7} \times 14^2 \times 18 = \frac{1}{3} \times \frac{22}{7} \times 196 \times 18$$ Calculate: $$V_{cone} = \frac{1}{3} \times \frac{22}{7} \times 3528 = \frac{1}{3} \times 11088 = 3696 \text{ cm}^3$$ 5. **Step 3: Calculate the volume of the cone part in contact with water** The water fills the space between the cylinder and the cone inside it. The volume of water is the volume of the cylinder minus the volume of the cone part submerged in water. 6. **Step 4: Calculate the volume of the cone part not in contact with water** Since the water height is 19 cm and the cone depth is 18 cm, the cone is fully submerged in water. However, the water height is greater than the cone depth, so the volume of water includes the entire cone volume plus some extra water above the cone. The volume of the cone part not in contact with water is the volume of the cone above the water level. Since the cone is only 18 cm deep and water is 19 cm high, the cone is fully submerged, so the volume of the cone not in contact with water is zero. **But the problem states the water completely fills the space between the cylinder and part of the cone inside the tin, so the volume of the cone not in contact with water is the volume of the cone above the water level inside the cone.** 7. **Step 5: Find the height of the cone above the water level** Since the cone is inserted 18 cm deep and water height is 19 cm, the water level is 1 cm above the top of the cone inside the cylinder. So the cone is fully submerged. 8. **Step 6: Calculate the volume of the cone part not in contact with water** Since the cone is fully submerged, the volume of the cone part not in contact with water is zero. **Final answer:** $$\boxed{0.0 \text{ cm}^3}$$