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Calculate the volume of a cylindrical tank with a diameter of 850 mm and a height of 1200 mm.

Mathematics

ScanSolve AI Answer

Answer

713 litres\text{713 litres}

33.46 inches\text{33.46 inches}

Step-by-step solution

7 steps

3:

4.3.1)

  1. Calculate the radius (rr) from the given diameter (DD).

    r=D2=850 mm2=425 mmr = \frac{D}{2} = \frac{850 \text{ mm}}{2} = 425 \text{ mm}
  2. Use the formula for the volume of a cylinder, V=πr2hV = \pi r^2 h, with the calculated radius and given height (h=1200 mmh = 1200 \text{ mm}).

    V=π(425 mm)2(1200 mm)V = \pi (425 \text{ mm})^2 (1200 \text{ mm}) V=π(180625 mm2)(1200 mm)V = \pi (180625 \text{ mm}^2) (1200 \text{ mm}) V=216750000π mm3V = 216750000 \pi \text{ mm}^3 V≈216750000×3.1415926535... mm3V \approx 216750000 \times 3.1415926535... \text{ mm}^3 V≈680999999.99... mm3V \approx 680999999.99... \text{ mm}^3

    Rounding this to the nearest whole number gives:

    V≈681000000 mm3V \approx 681000000 \text{ mm}^3

    The problem states the volume is 713 443 840 mm3^3. 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 mm3^3 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 mm3V = 713443840 \text{ mm}^3 and h=1200 mmh = 1200 \text{ mm}:

    r2=Vπh=713443840π×1200r^2 = \frac{V}{\pi h} = \frac{713443840}{\pi \times 1200} r2=7134438403769.911184r^2 = \frac{713443840}{3769.911184} r2≈189240.00r^2 \approx 189240.00 r≈189240≈435 mmr \approx \sqrt{189240} \approx 435 \text{ mm}

    So, the diameter would be 2×435 mm=870 mm2 \times 435 \text{ mm} = 870 \text{ mm}.
    This indicates that the given diameter of 850 mm is inconsistent with the given volume of 713 443 840 mm3^3 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 mm3681000000 \text{ 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 mmD = 850 \text{ mm} and h=1200 mmh = 1200 \text{ mm}:

    V=π(8502)2×1200V = \pi \left(\frac{850}{2}\right)^2 \times 1200 V=π(425)2×1200V = \pi (425)^2 \times 1200 V=π×180625×1200V = \pi \times 180625 \times 1200 V=216750000π mm3V = 216750000 \pi \text{ mm}^3 V≈681000000 mm3V \approx 681000000 \text{ mm}^3

    The calculated volume is approximately 681000000 mm3681000000 \text{ mm}^3. This is how the volume would be calculated using the given diameter and height. The value 713443840 mm3713443840 \text{ mm}^3 provided in the question is likely based on a slightly different diameter or height.

    4.3.2)

  3. Convert the volume to litres.

    We will use the volume given in the problem statement, V=713443840 mm3V = 713 443 840 \text{ mm}^3, as it is the stated volume of the tank.
    Given: 1 litre=1000000 mm31 \text{ litre} = 1 000 000 \text{ mm}^3.

    Vlitres=713443840 mm31000000 mm3/litreV_{\text{litres}} = \frac{713 443 840 \text{ mm}^3}{1 000 000 \text{ mm}^3/\text{litre}} Vlitres=713.44384 litresV_{\text{litres}} = 713.44384 \text{ litres}
  4. Round the answer to the nearest litre.

    Vlitres≈713 litresV_{\text{litres}} \approx 713 \text{ litres}

    The volume of the tank is approximately 713 litres\boxed{\text{713 litres}}.

    4.3.3)

  5. Convert the diameter from millimetres to centimetres.

    Given diameter D=850 mmD = 850 \text{ mm}.

    Dcm=850 mm×1 cm10 mm=85 cmD_{\text{cm}} = 850 \text{ mm} \times \frac{1 \text{ cm}}{10 \text{ mm}} = 85 \text{ cm}
  6. Convert the diameter from centimetres to inches.

    Given: 1 inch=2.54 cm1 \text{ inch} = 2.54 \text{ cm}.

    Dinches=85 cm2.54 cm/inchD_{\text{inches}} = \frac{85 \text{ cm}}{2.54 \text{ cm/inch}} Dinches≈33.4645669... inchesD_{\text{inches}} \approx 33.4645669... \text{ inches}
  7. Round the answer to two decimal places.

    Dinches≈33.46 inchesD_{\text{inches}} \approx 33.46 \text{ inches}

    The diameter of the tank in inches is approximately 33.46 inches\boxed{\text{33.46 inches}}.

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