To find the missing edge of a rectangular prism (a box shape), we use the formula for volume:
Volume = Length × Width × Height
If you know the Volume and two of the edges, you can find the third one by dividing the Volume by the product of the two known edges.
Formula:
Missing Edge = Volume ÷ (Known Edge 1 × Known Edge 2)
Let's solve each problem step-by-step:
1. Top Left Box
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Given: Volume = 512 cm³, Length = 8 cm, Width = 8 cm
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Step 1: Multiply the known edges: $8 \times 8 = 64$
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Step 2: Divide the volume by that number: $512 \div 64 = 8$
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Height: 8 cm
2. Top Middle Box
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Given: Volume = 315 cm³, Width = 7 cm, Height = 5 cm
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Step 1: Multiply the known edges: $7 \times 5 = 35$
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Step 2: Divide the volume by that number: $315 \div 35 = 9$
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Length: 9 cm
3. Top Right Box
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Given: Volume = 160 cm³, Length = 5 cm, Height = 4 cm
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Step 1: Multiply the known edges: $5 \times 4 = 20$
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Step 2: Divide the volume by that number: $160 \div 20 = 8$
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Width: 8 cm
4. Middle Left Box
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Given: Volume = 100 cm³, Length = 5 cm, Height = 4 cm
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Step 1: Multiply the known edges: $5 \times 4 = 20$
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Step 2: Divide the volume by that number: $100 \div 20 = 5$
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Width: 5 cm
5. Middle Center Box
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Given: Volume = 90 cm³, Length = 2 cm, Width = 5 cm
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Step 1: Multiply the known edges: $2 \times 5 = 10$
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Step 2: Divide the volume by that number: $90 \div 10 = 9$
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Height: 9 cm
6. Middle Right Box
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Given: Volume = 60 cm³, Width = 4 cm, Height = 3 cm
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Step 1: Multiply the known edges: $4 \times 3 = 12$
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Step 2: Divide the volume by that number: $60 \div 12 = 5$
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Length: 5 cm
7. Bottom Left Box
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Given: Volume = 72 cm³, Width = 4 cm, Height = 3 cm
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Step 1: Multiply the known edges: $4 \times 3 = 12$
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Step 2: Divide the volume by that number: $72 \div 12 = 6$
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Length: 6 cm
8. Bottom Middle Box
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Given: Volume = 504 cm³, Length = 9 cm, Height = 7 cm
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Step 1: Multiply the known edges: $9 \times 7 = 63$
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Step 2: Divide the volume by that number: $504 \div 63 = 8$
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Width: 8 cm
9. Bottom Right Box
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Given: Volume = 175 cm³, Length = 5 cm, Width = 5 cm
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Step 1: Multiply the known edges: $5 \times 5 = 25$
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Step 2: Divide the volume by that number: $175 \div 25 = 7$
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Height: 7 cm
Final Answer:
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
Parent Tip: Review the logic above to help your child master the concept of volume worksheet 6th grade.
