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.
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Here's the solution for question 13 a) and c): 13 a) Given: Cylindrical container 1: Diameter D_1 = 15 cm, Depth h_1 = 20 cm Cylindrical jar 2: Diameter D_2 = 10 cm Step 1: Calculate the radius for each cylinder. For container 1: r_1 = (D_1)/(2) = (15)/(2) = 7.5 cm For jar 2: r_2 = (D_2)/(2) = (10)/(2) = 5 cm Step 2: Calculate the volume of water in container 1. The volume of a cylinder is given by V = r^2 h. V_1 = r_1^2 h_1 V_1 = (7.5 cm)^2 (20 cm) V_1 = (56.25 cm^2) (20 cm) V_1 = 1125 cm^3 Step 3: Use the conservation of volume to find the depth in jar 2. When the water is poured into jar 2, its volume remains the same, so V_2 = V_1. Let h_2 be the depth of water in jar 2. V_2 = r_2^2 h_2 1125 cm^3 = (5 cm)^2 h_2 1125 cm^3 = 25 cm^2 h_2 Divide both sides by 25 : h_2 = 1125 cm^325 cm^2 h_2 = (1125)/(25) cm h_2 = 45 cm The depth of the water in the jar is 45 cm. 13 c) Given: Cylindrical tank: Diameter D = 5.0 m, Volume of water V = 110 000 dm^3 Step 1: Convert all measurements to consistent units. Let's convert everything to meters. Radius r = (D)/(2) = 5.0 m2 = 2.5 m Volume V = 110 000 dm^3. Since 1 m = 10 dm, then 1 m^3 = (10 dm)^3 = 1000 dm^3. V = 110 000 dm^31000 dm^3/m^3 = 110 m^3 Step 2: Use the volume formula to find the height of the water. The volume of a cylinder is V = r^2 h. We need to find h. Using = (22)/(7): 110 m^3 = (22)/(7) × (2.5 m)^2 × h 110 m^3 = (22)/(7) × 6.25 m^2 × h h = 110 m^3 × 722 × 6.25 m^2 h = (770)/(137.5) m h = 5.6 m The height of the water in the tank is 5.6 m. That's 2 down. 3 left today — send the next one.