Volume of 3D Shapes interactive worksheet - Free Printable

Let’s solve each 3D shape one by one, calculating the area of the base and then the volume, using standard volume formulas.

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🔹 Shape 1: Cube (Orange)

- Side length = 3 m

✔ Area of base = side × side = 3 m × 3 m = 9 m²

✔ Volume = side³ = 3 × 3 × 3 = 27 m³

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🔹 Shape 2: Rectangular Prism (Pink)

- Length = 4 cm, Width = 2 cm, Height = 2 cm

✔ Area of base = length × width = 4 cm × 2 cm = 8 cm²

✔ Volume = length × width × height = 4 × 2 × 2 = 16 cm³

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🔹 Shape 3: Square Pyramid

- Base side = 8 cm, Height = 9 cm

✔ Area of base = side × side = 8 cm × 8 cm = 64 cm²

✔ Volume = (1/3) × base area × height = (1/3) × 64 × 9
= (64 × 9) ÷ 3 = 576 ÷ 3 = 192 cm³

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🔹 Shape 4: Cylinder (Green)

- Diameter = 8 in → Radius = 4 in, Height = 12 in

✔ Area of base = π × r² = π × 4² = 16π in²
*(You can leave it as 16π or approximate as 50.27 in² if needed — but since no instruction to approximate, we’ll keep it exact.)*

✔ Volume = base area × height = 16π × 12 = 192π in³
*(Approximate: 192 × 3.1416 ≈ 603.19 in³)*

> 💡 *Note: Since the worksheet doesn’t specify to use π ≈ 3.14, it’s safest to leave answers in terms of π unless told otherwise.*

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🔹 Shape 5: Triangular Prism

- Base triangle: base = 4 cm, height = 3 cm → so area = (1/2)×4×3 = 6 cm²
- Length (prism height) = 11 cm

✔ Area of base = (1/2) × base × height = (1/2) × 4 × 3 = 6 cm²

✔ Volume = base area × prism height = 6 × 11 = 66 cm³

*(Note: The 5 cm shown is the hypotenuse of the triangle — not needed for area or volume.)*

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🔹 Shape 6: Trapezoidal Prism

- Bases of trapezoid: 8 cm and 14 cm, height of trapezoid = 4 cm
- Length (prism height) = 10 cm

✔ Area of base (trapezoid) = (1/2) × (sum of parallel sides) × height
= (1/2) × (8 + 14) × 4 = (1/2) × 22 × 4 = 11 × 4 = 44 cm²

✔ Volume = base area × prism height = 44 × 10 = 440 cm³

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## ✔ Final Answers:

Row 1:

- Cube:
Area of base = 9 m²
Volume = 27 m³

- Rectangular Prism:
Area of base = 8 cm²
Volume = 16 cm³

- Square Pyramid:
Area of base = 64 cm²
Volume = 192 cm³

Row 2:

- Cylinder:
Area of base = 16π in² *(or ~50.27 in²)*
Volume = 192π in³ *(or ~603.19 in³)*

- Triangular Prism:
Area of base = 6 cm²
Volume = 66 cm³

- Trapezoidal Prism:
Area of base = 44 cm²
Volume = 440 cm³

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✔ All calculations are complete! Let me know if you’d like them rounded or with π approximated.