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
Step 1: Calculate the volume of the spherical container. The diameter of the spherical container is 30 cm, so its radius r_s is (30)/(2) = 15 cm. The formula for the volume of a sphere is V_s = (4)/(3) r_s^3. V_s = (4)/(3) (15 cm)^3 V_s = (4)/(3) (3375 cm^3) V_s = 4 (1125 cm^3) V_s = 4500 cm^3 Step 2: Calculate the volume of water in the spherical container. The spherical container is (3)/(4) full of water. The volume of water V_w is (3)/(4) of the total volume of the sphere. V_w = (3)/(4) × 4500 cm^3 V_w = 3 × 1125 cm^3 V_w = 3375 cm^3 Step 3: Calculate the depth of the water in the cylindrical container. The water is emptied into a cylindrical container with a diameter of 12 cm. The radius of the cylindrical container r_c is (12)/(2) = 6 cm. The formula for the volume of a cylinder is V_c = r_c^2 h, where h is the depth of the water. Since the volume of water remains the same, V_w = V_c. 3375 cm^3 = (6 cm)^2 h 3375 cm^3 = 36 cm^2 h Divide both sides by 36 cm^2 to solve for h: h = 3375 cm^336 cm^2 h = (3375)/(36) cm h = 93.75 cm The depth of the water in the cylindrical container is 93.75 cm. Last free one today — make it count tomorrow, or type /upgrade for unlimited.