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Calculate the volume of each of these solids correct to three decimal places.

Mathematics

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Answers

3 parts
a

2262.000 cm32262.000 \text{ cm}^3

b

633.750 mm3633.750 \text{ mm}^3

c

5582.375 m35582.375 \text{ m}^3

Step-by-step solution

11 steps

1. Calculate the volume of each of these solids correct to three decimal places.

Part a· 3 steps

  1. Identify the shape and dimensions.

    The solid is a cuboid with length l=29l = 29 cm, width w=13w = 13 cm, and height h=6h = 6 cm.

  2. Apply the formula for the volume of a cuboid.

    The volume VV of a cuboid is given by the formula:

    V=l×w×hV = l \times w \times h

  3. Substitute the values and calculate.

    V=29 cm×13 cm×6 cmV = 29 \text{ cm} \times 13 \text{ cm} \times 6 \text{ cm} V=2262 cm3V = 2262 \text{ cm}^3

    Rounding to three decimal places:

    2262.000 cm3\boxed{2262.000 \text{ cm}^3}

Part b

633.750 mm3633.750 \text{ mm}^3

  1. Identify the shape and dimensions.

    The solid is a cuboid with length l=15l = 15 mm and height h=6.5h = 6.5 mm. The width is not explicitly given in the diagram.

  2. Make an assumption for the missing dimension.

    Based on the visual representation, we assume the width ww is equal to the height h=6.5h = 6.5 mm.

  3. Apply the formula for the volume of a cuboid.

    The volume VV of a cuboid is given by the formula:

    V=l×w×hV = l \times w \times h

  4. Substitute the values and calculate.

    V=15 mm×6.5 mm×6.5 mmV = 15 \text{ mm} \times 6.5 \text{ mm} \times 6.5 \text{ mm} V=633.75 mm3V = 633.75 \text{ mm}^3

    Rounding to three decimal places:

    633.750 mm3\boxed{633.750 \text{ mm}^3}

Part c

5582.375 m35582.375 \text{ m}^3

  1. Identify the shape and dimensions.

    The solid is a prism with a trapezoidal base.
    The parallel sides of the trapezoidal base are a=19a = 19 m and b=(19−2.5)b = (19 - 2.5) m.
    The height of the trapezoid is ht=8.5h_t = 8.5 m.
    The length of the prism is L=37L = 37 m.

  2. Calculate the length of the second parallel side of the trapezoid.

    b=19 m−2.5 m=16.5 mb = 19 \text{ m} - 2.5 \text{ m} = 16.5 \text{ m}

  3. Calculate the area of the trapezoidal base.

    The area AtA_t of a trapezoid is given by the formula:

    At=12(a+b)htA_t = \frac{1}{2} (a + b) h_t At=12(19 m+16.5 m)×8.5 mA_t = \frac{1}{2} (19 \text{ m} + 16.5 \text{ m}) \times 8.5 \text{ m} At=12(35.5 m)×8.5 mA_t = \frac{1}{2} (35.5 \text{ m}) \times 8.5 \text{ m} At=150.875 m2A_t = 150.875 \text{ m}^2

  4. Calculate the volume of the prism.

    The volume VV of a prism is given by the formula:

    V=At×LV = A_t \times L V=150.875 m2×37 mV = 150.875 \text{ m}^2 \times 37 \text{ m} V=5582.375 m3V = 5582.375 \text{ m}^3

    Rounding to three decimal places:

    5582.375 m3\boxed{5582.375 \text{ m}^3}
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