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Identify the circumference of the circle.

Mathematics

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7.1 If the 300 cm side of the rectangular tin plate is bent to form a circle, determine the diameter of the cylindrical tank. You may use the formula: Circumference of a circle = π×\pi \times diameter; Using π=3.14\pi = 3.14.

  1. Identify the circumference of the circle.

    When the 300 cm side of the rectangular tin plate is bent to form a circle, this length becomes the circumference (CC) of the circle.

    C=300 cmC = 300 \text{ cm}
  2. Use the given formula for the circumference of a circle.

    C=π×DC = \pi \times D

    Where DD is the diameter and π=3.14\pi = 3.14.

  3. Substitute the values and solve for the diameter (DD).

    300 cm=3.14×D300 \text{ cm} = 3.14 \times D D=300 cm3.14D = \frac{300 \text{ cm}}{3.14} D≈95.5414 cmD \approx 95.5414 \text{ cm}

    Rounding to two decimal places:

    D≈95.54 cmD \approx 95.54 \text{ cm}

    The diameter of the cylindrical tank is 95.54 cm\boxed{\text{95.54 cm}}.

    7.2 Calculate the volume of water that the cylindrical tank can hold in litres. You may use the formula: Volume of a cylindrical tank = π×r2×\pi \times r^2 \times height; Using π=3.14\pi = 3.14 and 1000 cm3=1 litre1000 \text{ cm}^3 = 1 \text{ litre}.

  4. Determine the radius (rr) and height (hh) of the cylindrical tank.

    From 7.1, the diameter (DD) is approximately 95.5414 cm95.5414 \text{ cm}.
    The radius (rr) is half of the diameter:

    r=D2=95.5414 cm2=47.7707 cmr = \frac{D}{2} = \frac{95.5414 \text{ cm}}{2} = 47.7707 \text{ cm}

    The height (hh) of the cylindrical tank is the other dimension of the rectangular plate:

    h=250 cmh = 250 \text{ cm}
  5. Calculate the volume of the cylindrical tank using the formula V=πr2hV = \pi r^2 h.

    Using π=3.14\pi = 3.14:

    V=3.14×(47.7707 cm)2×250 cmV = 3.14 \times (47.7707 \text{ cm})^2 \times 250 \text{ cm} V=3.14×2282.038 cm2×250 cmV = 3.14 \times 2282.038 \text{ cm}^2 \times 250 \text{ cm} V=3.14×570509.5 cm3V = 3.14 \times 570509.5 \text{ cm}^3 V≈1791799.83 cm3V \approx 1791799.83 \text{ cm}^3
  6. Convert the volume from cubic centimeters to litres.

    Given 1000 cm3=1 litre1000 \text{ cm}^3 = 1 \text{ litre}.

    Vlitres=1791799.83 cm31000 cm3/litreV_{\text{litres}} = \frac{1791799.83 \text{ cm}^3}{1000 \text{ cm}^3/\text{litre}} Vlitres≈1791.79983 litresV_{\text{litres}} \approx 1791.79983 \text{ litres}

    Rounding to the nearest litre:

    Vlitres≈1792 litresV_{\text{litres}} \approx 1792 \text{ litres}

    The volume of water the cylindrical tank can hold is approximately 1792 litres\boxed{\text{1792 litres}}.

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