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Mathematics

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Step-by-step solution

3 steps

The question asks for the volume of each stack of cubes, where each small cube represents 1 cubic centimeter. To find the volume, we count the number of individual cubes in each stack.

  1. Calculate the volume for stack a).

    Count the cubes in stack a).

    • Bottom layer: 3 cubes
    • Top layer: 2 cubes Total number of cubes = 3+2=53 + 2 = 5 cubes. The volume is 5 cubic centimeters.
  2. Calculate the volume for stack b).

    Count the cubes in stack b).

    • Bottom layer: There are 2 cubes in the front row and 2 cubes in the back row, making a 2×22 \times 2 base. So, 2×2=42 \times 2 = 4 cubes.
    • Top layer: 2 cubes Total number of cubes = 4+2=64 + 2 = 6 cubes. The volume is 6 cubic centimeters.
  3. Calculate the volume for stack c).

    Count the cubes in stack c).

    • Bottom layer: There are 3 cubes in the front row, 3 in the middle row, and 3 in the back row, making a 3×33 \times 3 base. So, 3×3=93 \times 3 = 9 cubes.
    • Middle layer: There are 2 cubes in the front row and 2 cubes in the back row, making a 2×22 \times 2 layer. So, 2×2=42 \times 2 = 4 cubes.
    • Top layer: 1 cube Total number of cubes = 9+4+1=149 + 4 + 1 = 14 cubes. The volume is 14 cubic centimeters.

    The volumes for each stack are:

    a) 5 cubic centimeters\boxed{\text{5 cubic centimeters}}

    b) 6 cubic centimeters\boxed{\text{6 cubic centimeters}}

    c) 14 cubic centimeters\boxed{\text{14 cubic centimeters}}

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