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
Welcome back Innocent — missed you this week. Here are the solutions for question 4.3: 4.3.1) Step 1: Calculate the radius (r) from the given diameter (D). r = (D)/(2) = 850 mm2 = 425 mm Step 2: Use the formula for the volume of a cylinder, V = r^2 h, with the calculated radius and given height (h = 1200 mm). V = (425 mm)^2 (1200 mm) V = (180625 mm^2) (1200 mm) V = 216750000 mm^3 V ≈ 216750000 × 3.1415926535... mm^3 V ≈ 680999999.99... mm^3 Rounding this to the nearest whole number gives: V ≈ 681000000 mm^3 The problem states the volume is 713 443 840 mm^3. There seems to be a slight discrepancy between the given volume and the volume calculated using the given diameter and height. However, following the instruction to "show how the volume was calculated if this tank has a diameter of 850 mm", we perform the calculation as above. If we assume the given volume of 713 443 840 mm^3 is correct, then the diameter of 850 mm might be an approximation or there's a slight error in the problem statement. For the purpose of "showing how it was calculated", we use the provided diameter and height. Let's re-evaluate the calculation with the given volume and height to find the radius, then compare it to the 850 mm diameter. If V = 713443840 mm^3 and h = 1200 mm: r^2 = (V)/( h) = (713443840)/( × 1200) r^2 = (713443840)/(3769.911184) r^2 ≈ 189240.00 r ≈ sqrt(189240) ≈ 435 mm So, the diameter would be 2 × 435 mm = 870 mm. This indicates that the given diameter of 850 mm is inconsistent with the given volume of 713 443 840 mm^3 and height of 1200 mm. Given the instruction "Show how the volume was calculated if this tank has a diameter of 850 mm", we must use the 850 mm diameter. The calculated volume is approximately 681000000 mm^3. The question implies that the given volume was calculated using the given diameter and height, but our calculation shows a difference. We will proceed with the calculation based on the provided diameter and height. Using D = 850 mm and h = 1200 mm: V = ((850)/(2))^2 × 1200 V = (425)^2 × 1200 V = × 180625 × 1200 V = 216750000 mm^3 V ≈ 681000000 mm^3 The calculated volume is approximately 681000000 mm^3. This is how the volume would be calculated using the given diameter and height. The value 713443840 mm^3 provided in the question is likely based on a slightly different diameter or height. 4.3.2) Step 1: Convert the volume to litres. We will use the volume given in the problem statement, V = 713 443 840 mm^3, as it is the stated volume of the tank. Given: 1 litre = 1 000 000 mm^3. V_litres = 713 443 840 mm^31 000 000 mm^3/litre V_litres = 713.44384 litres Step 2: Round the answer to the nearest litre. V_litres ≈ 713 litres The volume of the tank is approximately 713 litres. 4.3.3) Step 1: Convert the diameter from millimetres to centimetres. Given diameter D = 850 mm. D_cm = 850 mm × 1 cm10 mm = 85 cm Step 2: Convert the diameter from centimetres to inches. Given: 1 inch = 2.54 cm. D_inches = 85 cm2.54 cm/inch D_inches ≈ 33.4645669... inches Step 3: Round the answer to two decimal places. D_inches ≈ 33.46 inches The diameter of the tank in inches is approximately 33.46 inches. Send me the next one 📸