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: Identify the dimensions of the conical container. The base radius of the conical container is r_c = 21 cm. The height of the conical container is h_c = 30 cm. Step 2: Calculate the volume of water in the conical container. The formula for the volume of a cone is V_c = (1)/(3) r_c^2 h_c. V_c = (1)/(3) × × (21 cm)^2 × 30 cm V_c = (1)/(3) × × 441 cm^2 × 30 cm V_c = × 441 cm^2 × 10 cm V_c = 4410 cm^3 Step 3: Identify the dimensions of the cylindrical container. The radius of the cylindrical container is r_cyl = 7 cm. Let the depth of water in the cylinder be h_cyl. Step 4: Equate the volume of water from the cone to the volume of water in the cylinder. When the water from the cone is emptied into the cylinder, the volume of water remains the same. The formula for the volume of water in the cylinder is V_cyl = r_cyl^2 h_cyl. So, V_cyl = V_c. r_cyl^2 h_cyl = 4410 cm^3 Step 5: Substitute the cylinder's radius and solve for the depth of water (h_cyl). × (7 cm)^2 × h_cyl = 4410 cm^3 × 49 cm^2 × h_cyl = 4410 cm^3 Divide both sides by : 49 cm^2 × h_cyl = 4410 cm^3 h_cyl = 4410 cm^349 cm^2 h_cyl = 90 cm The depth of water in the cylinder is 90 cm. 3 done, 2 left today. You're making progress.