I'll work through each problem step by step to verify the solutions shown in this answer key.
Problem 1: Green Cube (3m × 3m × 3m)
*Volume:*
- Formula: V = s³
- Calculation: V = 3³ = 3 × 3 × 3 = 27 m³ ✓
*Surface Area:*
- Formula: S = 6s²
- Calculation: S = 6(3)² = 6 × 9 = 54 m² ✓
Problem 2: Yellow Rectangular Prism (36cm × 16cm × 16cm)
*Volume:*
- Formula: V = l × w × h
- Calculation: V = 36 × 16 × 16
- Let me verify: 36 × 16 = 576, then 576 × 16 = 9,216 cm³ ✓
*Surface Area:*
- Formula: S = 2(lw + lh + wh)
- lw = 36 × 16 = 576
- lh = 36 × 16 = 576
- wh = 16 × 16 = 256
- Sum: 576 + 576 + 256 = 1,408
- S = 2 × 1,408 = 2,816 cm² ✓
Problem 3: Purple Rectangular Prism (8in × 4in × 7in)
*Volume:*
- Formula: V = l × w × h
- Calculation: V = 8 × 4 × 7 = 32 × 7 = 224 in³ ✓
*Surface Area:*
- Formula: S = 2(lw + lh + wh)
- lw = 8 × 4 = 32
- lh = 8 × 7 = 56
- wh = 4 × 7 = 28
- Sum: 32 + 56 + 28 = 116
- S = 2 × 116 = 232 in² ✓
Problem 4: Blue Cube (20mm × 20mm × 20mm)
*Volume:*
- Formula: V = s³
- Calculation: V = 20³ = 20 × 20 × 20 = 8,000 mm³ ✓
*Surface Area:*
- Formula: S = 6s²
- Calculation: S = 6(20)² = 6 × 400 = 2,400 mm² ✓
All calculations have been verified and are correct!
Final Answer: All answers in the worksheet are correct:
- Green cube: Volume = 27 m³, Surface Area = 54 m²
- Yellow prism: Volume = 9,216 cm³, Surface Area = 2,816 cm²
- Purple prism: Volume = 224 in³, Surface Area = 232 in²
- Blue cube: Volume = 8,000 mm³, Surface Area = 2,400 mm²
Parent Tip: Review the logic above to help your child master the concept of geometry surface area and volume worksheet answers.
