This problem tests your ability to work with fractions and perform multi-step calculations involving volume. When you see a question about filling containers with unit cubes, remember that volume equals the number of unit cubes that fit inside.

Let's work through this step by step. The box holds exactly 36 unit cubes when completely full. First, find how many cubes are in the box when it's $$\frac{5}{6}$$ full: $$\frac{5}{6} \times 36 = 30$$ unit cubes. Then Ms. Rodriguez removes 8 cubes, so you subtract: $$30 - 8 = 22$$ unit cubes remaining. The volume is 22 cubic units.

Looking at the wrong answers: Choice A (20 cubic units) likely comes from incorrectly calculating $$\frac{5}{6}$$ of 36 as 28, then subtracting 8 to get 20. Choice B (30 cubic units) is the trap of forgetting to subtract the 8 cubes that were removed—this gives you only the first step of the problem. Choice C (28 cubic units) probably results from miscalculating $$\frac{5}{6} \times 36$$ as 28 instead of 30, possibly by confusing it with $$\frac{7}{9} \times 36$$.

When solving multi-step word problems like this, always identify each operation in order: first find the fraction of the total, then apply any additions or subtractions. Don't skip steps, and double-check your fraction multiplication by ensuring your answer makes sense compared to the original amount.

When you see a problem about finding the volume of a structure made from unit cubes, remember that volume measures how much space the entire structure occupies. Since each unit cube has a volume of 1 cubic unit, you need to count the total number of cubes in the whole tower.

To find the total volume, you add up all the unit cubes in every layer: bottom layer (9 cubes) + middle layer (6 cubes) + top layer (3 cubes) + new top layer (2 cubes) = $$9 + 6 + 3 + 2 = 20$$ unit cubes. Since each unit cube has a volume of 1 cubic unit, the total volume is 20 cubic units.

Choice A incorrectly multiplies the numbers of cubes in each layer ($$9 × 6 × 3 × 2 = 324$$). This mistake happens when students confuse volume calculations for rectangular prisms (length × width × height) with counting individual unit cubes. Here, the layers are stacked on top of each other, not arranged in a rectangular grid.

Choice B only counts the original three layers ($$9 + 6 + 3 = 18$$) and ignores the new layer Tom added. Always read carefully to include all parts mentioned in the problem.

Choice D adds an extra 2 cubes ($$9 + 6 + 3 + 2 + 2 = 22$$) beyond what the problem states. This likely comes from misreading "adds one more layer on top with 2 unit cubes" as adding 2 layers or adding 2 extra cubes.

Remember: For structures made of unit cubes, volume equals the total count of all cubes. Add them up layer by layer, and don't multiply unless you're finding the volume of a solid rectangular prism.

Volume equals the total number of unit cubes that pack the figure. Adding all unit cubes: 8 + 6 + 4 = 18 unit cubes total, so volume is 18 cubic units. Choice A only counts the bottom layer. Choice C multiplies the layer sizes instead of adding them. Choice D incorrectly calculates an average using only the bottom layer size.

The second container has the same capacity as the first: 27 unit cubes when full. When filled 2/3 full: 27 × 2/3 = 18 unit cubes. The volume is 18 cubic units. Choice B calculates 27 × 1/3 instead of 2/3. Choice C incorrectly adds 27 + 9. Choice D uses an incorrect fraction calculation.

Volume counts the cubic units that form the structure of a solid. Filling space without gaps involves stacking unit cubes tightly to occupy the figure fully, with no overlaps. Each layer's cubes connect to the total volume by adding up to the whole amount. To count, sum the cubes in each layer, like 3 per layer for three layers totaling 9. A common misconception is that volume is based on layers or visible faces, but it's the total cubes. Cubic units offer a consistent way to measure volume across shapes. This method generalizes to all solids, emphasizing complete filling.

Volume counts the number of cubic units that make up a solid figure. The unit cubes fill the space of the solid completely without any gaps or overlaps. Each unit cube adds one cubic unit to the total volume, so for this figure with 12 cubes in the bottom and 4 on top, the total is 16 cubic units. To count the volume, add the number of cubes in each layer: 12 + 4 = 16. A common misconception is to count only outside or visible cubes, but all internal cubes must be included. Cubic units measure the three-dimensional space occupied by any solid. This method allows us to correct reasoning errors about volume measurement.

Volume is calculated by counting the cubic units inside a solid. Filling without gaps means using unit cubes to pack the space entirely, preventing overlaps or empty spots. The cubes collectively determine the total volume through their combined count. Counting requires including every cube used in the construction, regardless of position. A misconception is confusing volume with surface area or outside squares, but volume is about internal space. Generally, cubic units standardize how we measure three-dimensional space. They allow for broad application in determining volumes of various objects.

Volume counts the cubic units required to build or fill a solid. Filling without gaps means packing unit cubes completely, ensuring no overlaps or empty spaces remain. Each cube adds to the total volume, connecting the parts to the whole measurement. To count accurately, include every unit cube, even if hidden inside the solid. A misconception is that only visible cubes contribute to volume, but all cubes fill space. Cubic units allow for standardized volume assessment in three dimensions. This approach generalizes to measuring any solid's capacity effectively.

Volume measures the amount of space a solid figure occupies by counting the number of cubic units it contains. The unit cubes in each solid must fill their respective spaces without gaps or overlaps for an accurate comparison of volumes. Solid A with 2 layers of 6 cubes each totals 12 cubic units, while Solid B with 3 layers of 4 cubes each also totals 12, showing equal volumes through the total cube count. Counting involves multiplying cubes per layer by the number of layers for each solid and comparing the results. A misconception is that more layers always mean greater volume, but it depends on the cubes per layer. Cubic units standardize volume measurement across different shapes and sizes. Ultimately, this method helps in understanding that rearranged cubes can maintain the same volume if the total count remains unchanged.

Volume counts the number of cubic units that make up a solid figure. The unit cubes fill the space of the solid completely without any gaps or overlaps. Each unit cube adds one cubic unit to the total volume, so Solid A with 10 cubes has 10 cubic units and Solid B with 12 has 12 cubic units, making B larger. To count the volume, simply total the number of unit cubes in each solid. A common misconception is that shape or height affects volume more than the total cubes, but it's solely the number of cubes that matters. Cubic units measure the three-dimensional space occupied by any solid. This method allows us to compare volumes of different figures accurately.