To find the volume of each shape, we count the total number of cubes. Since hidden cubes are needed to support the ones on top, we can count layer by layer (from bottom to top) or column by column.
Here is the step-by-step count for each shape:
1.
*
Bottom Layer: There is a back row of 3, a middle row of 2, and a front cube on the left. Total = $3 + 2 + 1 = 6$.
*
Middle Layer: There is a back row of 3 and one cube on the left. Total = $3 + 1 = 4$.
*
Top Layer: There are 2 cubes in the back. Total = 2.
*
Total Volume: $6 + 4 + 2 = 12$ cubic units.
2.
*
Bottom Layer: A full $2 \times 3$ rectangle. Total = 6.
*
Middle Layer: Two columns of 2 cubes high at the back-left. Total = 2.
*
Top Layer: One single cube on top. Total = 1.
*
Total Volume: $6 + 2 + 1 = 9$ cubic units.
3.
*
Bottom Layer: An L-shape with 4 cubes.
*
Top Layer: 1 cube sitting on the corner.
*
Total Volume: $4 + 1 = 5$ cubic units.
4.
* This shape is a large block with a piece missing from the front-right corner.
* Imagine the full block is 4 cubes wide, 3 cubes deep, and 4 cubes high. That would be $4 \times 3 \times 4 = 48$ cubes.
* The missing part is a block that is 2 cubes wide, 1 cube deep, and 2 cubes high. That is $2 \times 1 \times 2 = 4$ cubes.
*
Total Volume: $48 - 4 = 44$ cubic units.
5.
*
Bottom Layer: A $2 \times 4$ rectangle. Total = 8.
*
Top Layer: A row of 3 cubes along the back. Total = 3.
*
Total Volume: $8 + 3 = 11$ cubic units.
6.
*
Bottom Layer: Count all the footprints. There are 3 in the front row, 3 in the middle, and 3 in the back. Total = 9.
*
Middle Layer: A $2 \times 3$ block sits on the back half. Total = 6.
*
Top Layer: Another $2 \times 3$ block sits on top of that. Total = 6.
*
Total Volume: $9 + 6 + 6 = 21$ cubic units.
7.
*
Bottom Layer: 3 cubes in an L-shape.
*
Top Layer: 1 cube.
*
Total Volume: $3 + 1 = 4$ cubic units.
8.
*
Bottom Layer: An L-shape made of 4 cubes.
*
Middle Layer: 2 cubes stacked on the back-left corner.
*
Top Layer: 1 cube stacked on the very highest point.
*
Total Volume: $4 + 2 + 1 = 7$ cubic units.
9.
* This is a complete rectangular prism (a box shape).
* It is 4 cubes wide, 3 cubes deep, and 3 cubes high.
* Calculation: $4 \times 3 \times 3 = 36$.
*
Total Volume: 36 cubic units.
10.
*
Bottom Layer: A $2 \times 3$ rectangle. Total = 6.
*
Middle Layer: Same as the bottom ($2 \times 3$). Total = 6.
*
Top Layer: Same as the bottom ($2 \times 3$). Total = 6.
*
Very Top: 1 single cube in the center.
*
Total Volume: $6 + 6 + 6 + 1 = 19$ cubic units.
Final Answer:
1. 12 cubic units
2. 9 cubic units
3. 5 cubic units
4. 44 cubic units
5. 11 cubic units
6. 21 cubic units
7. 4 cubic units
8. 7 cubic units
9. 36 cubic units
10. 19 cubic units
Parent Tip: Review the logic above to help your child master the concept of finding volume of irregular shapes worksheet.
