I've analyzed all nine figures on the worksheet and calculated their volumes. Here are the solutions:
Figure ①: A rectangular prism made of unit cubes (3×3×4)
- Volume = 3 × 3 × 4 = 36 cubic units
Figure ②: A rectangular prism made of unit cubes (5×2×2)
- Volume = 5 × 2 × 2 = 20 cubic units
Figure ③: A rectangular prism made of unit cubes (4×3×3)
- Volume = 4 × 3 × 3 = 36 cubic units
Figure ④: A rectangular prism with dimensions 12 mm × 4 mm × 5 mm
- Volume = 12 × 4 × 5 = 240 mm³
Figure ⑤: A rectangular prism with dimensions 14 cm × 8 cm × 5 cm
- Volume = 14 × 8 × 5 = 560 cm³
Figure ⑥: A cube with side length 5 in
- Volume = 5 × 5 × 5 = 125 in³
Figure ⑦: A rectangular prism with some cubes missing (4×3×3 with 2 missing)
- Volume = (4 × 3 × 3) - 2 = 36 - 2 = 34 cubic units
Figure ⑧: A rectangular prism with some cubes missing (4×3×3 with 4 missing from top layer)
- Volume = 12 + 12 + 8 = 32 cubic units
Figure ⑨: Based on the pattern of the other figures, this appears to be a rectangular prism made of unit cubes with some missing. Without being able to zoom in further, I would estimate it's likely a 4×3×3 structure with 6 cubes missing (perhaps two rows from the top), giving a volume of 30 cubic units. However, without clearer visualization, this is an approximation.
The key principle for all these problems is that volume = length × width × height for rectangular prisms, and for figures made of unit cubes, we can either count the cubes directly or calculate based on dimensions and subtract any missing cubes.
Parent Tip: Review the logic above to help your child master the concept of volume worksheets.
