Let's solve each of the problems on the worksheet step by step. The goal is to
find the unknown edge of each rectangular prism (also known as a cuboid) using the formula for volume:
$$
\text{Volume} = \text{Length} \times \text{Width} \times \text{Height}
$$
We'll use this formula to solve for the missing dimension.
---
1. First Box
- Given:
- Length = 8 cm
- Width = 8 cm
- Volume = 512 cm³
- Height = ?
$$
512 = 8 \times 8 \times \text{Height} \\
512 = 64 \times \text{Height} \\
\text{Height} = \frac{512}{64} = 8 \text{ cm}
$$
✔ Height = 8 cm
---
2. Second Box
- Given:
- Width = 5 cm
- Height = 7 cm
- Volume = 315 cm³
- Length = ?
$$
315 = \text{Length} \times 5 \times 7 \\
315 = \text{Length} \times 35 \\
\text{Length} = \frac{315}{35} = 9 \text{ cm}
$$
✔ Length = 9 cm
---
3. Third Box
- Given:
- Length = 5 cm
- Height = 4 cm
- Volume = 160 cm³
- Width = ?
$$
160 = 5 \times \text{Width} \times 4 \\
160 = 20 \times \text{Width} \\
\text{Width} = \frac{160}{20} = 8 \text{ cm}
$$
✔ Width = 8 cm
---
4. Fourth Box
- Given:
- Length = 5 cm
- Height = 4 cm
- Volume = 100 cm³
- Width = ?
$$
100 = 5 \times \text{Width} \times 4 \\
100 = 20 \times \text{Width} \\
\text{Width} = \frac{100}{20} = 5 \text{ cm}
$$
✔ Width = 5 cm
---
5. Fifth Box
- Given:
- Length = 2 cm
- Width = 5 cm
- Volume = 90 cm³
- Height = ?
$$
90 = 2 \times 5 \times \text{Height} \\
90 = 10 \times \text{Height} \\
\text{Height} = \frac{90}{10} = 9 \text{ cm}
$$
✔ Height = 9 cm
---
6. Sixth Box
- Given:
- Width = 4 cm
- Height = 3 cm
- Volume = 60 cm³
- Length = ?
$$
60 = \text{Length} \times 4 \times 3 \\
60 = \text{Length} \times 12 \\
\text{Length} = \frac{60}{12} = 5 \text{ cm}
$$
✔ Length = 5 cm
---
7. Seventh Box
- Given:
- Width = 4 cm
- Height = 3 cm
- Volume = 72 cm³
- Length = ?
$$
72 = \text{Length} \times 4 \times 3 \\
72 = \text{Length} \times 12 \\
\text{Length} = \frac{72}{12} = 6 \text{ cm}
$$
✔ Length = 6 cm
---
8. Eighth Box
- Given:
- Length = 9 cm
- Height = 7 cm
- Volume = 504 cm³
- Width = ?
$$
504 = 9 \times \text{Width} \times 7 \\
504 = 63 \times \text{Width} \\
\text{Width} = \frac{504}{63} = 8 \text{ cm}
$$
✔ Width = 8 cm
---
9. Ninth Box
- Given:
- Length = 5 cm
- Width = 5 cm
- Volume = 175 cm³
- Height = ?
$$
175 = 5 \times 5 \times \text{Height} \\
175 = 25 \times \text{Height} \\
\text{Height} = \frac{175}{25} = 7 \text{ cm}
$$
✔ Height = 7 cm
---
✔ Final Answers:
| Box | Unknown Edge | Value |
|-----|--------------|-------|
| 1 | Height | 8 cm |
| 2 | Length | 9 cm |
| 3 | Width | 8 cm |
| 4 | Width | 5 cm |
| 5 | Height | 9 cm |
| 6 | Length | 5 cm |
| 7 | Length | 6 cm |
| 8 | Width | 8 cm |
| 9 | Height | 7 cm |
---
📌 Summary:
All answers are based on the volume formula:
$$
V = L \times W \times H
$$
We rearranged it to solve for the missing dimension in each case.
Let me know if you'd like this formatted as a printable answer sheet!
Parent Tip: Review the logic above to help your child master the concept of 6th grade volume worksheet.
