Identify the dimensions and components of the surface area in contact with water.

Step 1: Identify the dimensions and components of the surface area in contact with water. The container has an internal radius r = 10.5 cm. The water height is H = 30.5 cm. The base is hemispherical, so its height is equal to its radius, r = 10.5 cm. The height of the cylindrical part filled with water is h = H - r = 30.5 cm - 10.5 cm = 20 cm. The surface area in contact with water consists of three parts: 1. The curved surface area of the hemispherical base. 2. The curved surface area of the cylindrical part up to the water level. 3. The area of the water surface (a circular area at the top of the water). Step 2: Calculate the curved surface area of the hemispherical base. The formula for the curved surface area of a hemisphere is 2 r^2. A_hemisphere = 2 × (22)/(7) × (10.5 cm)^2 A_hemisphere = 2 × (22)/(7) × 110.25 cm^2 A_hemisphere = 44 × (110.25)/(7) cm^2 A_hemisphere = 44 × 15.75 cm^2 A_hemisphere = 693 cm^2 Step 3: Calculate the curved surface area of the cylindrical part in contact with water. The formula for the curved surface area of a cylinder is 2 r h. A_cylinder = 2 × (22)/(7) × 10.5 cm × 20 cm A_cylinder = 2 × (22)/(7) × (21)/(2) cm × 20 cm A_cylinder = 22 × 3 × 20 cm^2 A_cylinder = 66 × 20 cm^2 A_cylinder = 1320 cm^2 Step 4: Calculate the area of the water surface. The formula for the area of a circle is r^2. A_water\_surface = (22)/(7) × (10.5 cm)^2 A_water\_surface = (22)/(7) × 110.25 cm^2 A_water\_surface = 22 × 15.75 cm^2 A_water\_surface = 346.5 cm^2 Step 5: Calculate the total surface area in contact with water. The total surface area is the sum of the areas calculated in Steps 2, 3, and 4. A_total = A_hemisphere + A_cylinder + A_water\_surface A_total = 693 cm^2 + 1320 cm^2 + 346.5 cm^2 A_total = 2359.5 cm^2 The surface area of the container that is in contact with water is 2359.5 cm^2. That's 3 down. 2 left today — send the next one.