Let’s solve each problem step by step. We’ll use the correct volume formulas:
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Pyramid: Volume = (1/3) × base area × height
→ For square or rectangular base: base area = length × width
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Cone: Volume = (1/3) × π × r² × h
→ r = radius, h = height
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Sphere: Not in this worksheet — but if it were: (4/3)πr³
We are told to leave answers to 2 decimal places where necessary.
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Problem 1)
Square pyramid: base = 4 cm × 4 cm, height = 9 cm
Base area = 4 × 4 = 16 cm²
Volume = (1/3) × 16 × 9 = (1/3) × 144 =
48.00 cm³
✔ Check: 16 × 9 = 144; 144 ÷ 3 = 48 → Correct.
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Problem 2)
Rectangular pyramid: base = 12 cm × 6 cm, height = 15 cm
Base area = 12 × 6 = 72 cm²
Volume = (1/3) × 72 × 15 = (1/3) × 1080 =
360.00 cm³
✔ Check: 72 × 15 = 1080; 1080 ÷ 3 = 360 → Correct.
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Problem 3)
Rectangular pyramid: base = 5 cm × 7 cm, height = 20 cm
Base area = 5 × 7 = 35 cm²
Volume = (1/3) × 35 × 20 = (1/3) × 700 ≈
233.33 cm³
✔ Check: 35 × 20 = 700; 700 ÷ 3 = 233.333... → Rounded to 2 decimals: 233.33
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Problem 4)
Parent Tip: Review the logic above to help your child master the concept of eighth grade algebra worksheet.
