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Calculate the volume of the given rectangular prisms. a) L=4, W=2, H=3 b) L=3, W=3, H=3 c) L=5, W=3, H=3 d) L=4, W=3, H=3

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4 parts
a

24 cubic units\text{24 cubic units}

b

27 cubic units\text{27 cubic units}

c

45 cubic units\text{45 cubic units}

d

36 cubic units\text{36 cubic units}

Step-by-step solution

8 steps

To find the volume of each shape, we count the number of unit cubes along its length, width, and height, then multiply these dimensions.

Part a· 2 steps

  1. Determine the dimensions.

    The length is 4 units, the width is 2 units, and the height is 3 units.

  2. Calculate the volume.

    Volume=length×width×height=4×2×3=24 cubic units\text{Volume} = \text{length} \times \text{width} \times \text{height} = 4 \times 2 \times 3 = 24 \text{ cubic units}

    The volume of shape (a) is 24 cubic units\boxed{\text{24 cubic units}}.

Part b

27 cubic units\text{27 cubic units}

  1. Determine the dimensions.

    The length is 3 units, the width is 3 units, and the height is 3 units.

  2. Calculate the volume.

    Volume=length×width×height=3×3×3=27 cubic units\text{Volume} = \text{length} \times \text{width} \times \text{height} = 3 \times 3 \times 3 = 27 \text{ cubic units}

    The volume of shape (b) is 27 cubic units\boxed{\text{27 cubic units}}.

Part c

45 cubic units\text{45 cubic units}

  1. Determine the dimensions.

    The length is 5 units, the width is 3 units, and the height is 3 units.

  2. Calculate the volume.

    Volume=length×width×height=5×3×3=45 cubic units\text{Volume} = \text{length} \times \text{width} \times \text{height} = 5 \times 3 \times 3 = 45 \text{ cubic units}

    The volume of shape (c) is 45 cubic units\boxed{\text{45 cubic units}}.

Part d

36 cubic units\text{36 cubic units}

  1. Determine the dimensions.

    The length is 4 units, the width is 3 units, and the height is 3 units.

  2. Calculate the volume.

    Volume=length×width×height=4×3×3=36 cubic units\text{Volume} = \text{length} \times \text{width} \times \text{height} = 4 \times 3 \times 3 = 36 \text{ cubic units}

    The volume of shape (d) is 36 cubic units\boxed{\text{36 cubic units}}.

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