This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Here's how to determine the rise in the water level: Step 1: Calculate the volume of the spherical ball. The volume of a sphere is given by the formula V_sphere = (4)/(3) r^3. Given the radius of the spherical ball r = 1.5\, cm: V_sphere = (4)/(3) (1.5\, cm)^3 V_sphere = (4)/(3) (3.375\, cm^3) V_sphere = 4.5 \, cm^3 Step 2: Relate the volume of the sphere to the rise in water level in the cylindrical tin. When the spherical ball is immersed, it displaces a volume of water equal to its own volume. This displaced water causes the water level in the cylindrical tin to rise. Let h be the rise in the water level. The volume of this rise is a cylinder with the radius of the tin and height h. The volume of a cylinder is given by the formula V_cylinder = R^2 h. Given the radius of the cylindrical tin R = 1.8\, cm: V_rise = (1.8\, cm)^2 h V_rise = (3.24\, cm^2) h Step 3: Equate the volumes and solve for h. The volume of the sphere is equal to the volume of the water rise: V_sphere = V_rise 4.5 \, cm^3 = 3.24 \, cm^2 h Divide both sides by : 4.5\, cm^3 = 3.24\, cm^2 h Solve for h: h = 4.5\, cm^33.24\, cm^2 h ≈ 1.3888... \, cm Step 4: Round the answer to one decimal place. h ≈ 1.4\, cm The rise in the water level in the tin is 1.4 cm. Last free one today — make it count tomorrow, or type /upgrade for unlimited.