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Given formula for volume (V) = (pi d² h)/(4)

Mathematics

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Answer

0.2955 m30.2955 \text{ m}^3

Step-by-step solution

6 steps

  1. Identify the given values and formula.

    The solid shape is a cylinder.
    Given formula for volume (VV) = πd2h4\frac{\pi d^2 h}{4}
    Given diameter (dd) = 56 cm56 \text{ cm}
    Given height (hh) = 1.2 m1.2 \text{ m}
    Use π=3.14\pi = 3.14.

  2. Ensure consistent units.

    The diameter is in centimeters and the height is in meters. Convert the diameter to meters to match the height.

    d=56 cm=0.56 md = 56 \text{ cm} = 0.56 \text{ m}

  3. Substitute the values into the formula.

    V=3.14×(0.56 m)2×1.2 m4V = \frac{3.14 \times (0.56 \text{ m})^2 \times 1.2 \text{ m}}{4}

  4. Calculate the square of the diameter.

    (0.56 m)2=0.3136 m2(0.56 \text{ m})^2 = 0.3136 \text{ m}^2

  5. Perform the multiplication in the numerator.

    V=3.14×0.3136 m2×1.2 m4V = \frac{3.14 \times 0.3136 \text{ m}^2 \times 1.2 \text{ m}}{4} V=1.181952 m34V = \frac{1.181952 \text{ m}^3}{4}

  6. Divide to find the volume.

    V=0.295488 m3V = 0.295488 \text{ m}^3

    Rounding to a reasonable number of decimal places (e.g., four decimal places):

    0.2955 m30.2955 \text{ m}^3
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