Volume and Surface Area of Rectangular Prisms Worksheet | 7th ... - Free Printable

Let’s solve each problem step by step. We’ll calculate Volume and Surface Area for each shape.

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🔷 For Rectangular Prisms (Cuboids):

Formulas:
- Volume = length × width × height
- Surface Area = 2×(length×width + length×height + width×height)

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#### 1st Prism: 2cm × 3cm × 5cm

Volume:
2 × 3 × 5 = 6 × 5 = 30 cm³

Surface Area:
2×(2×3 + 2×5 + 3×5) = 2×(6 + 10 + 15) = 2×31 = 62 cm²

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#### 2nd Prism: 2cm × 9cm × 3cm

Volume:
2 × 9 × 3 = 18 × 3 = 54 cm³

Surface Area:
2×(2×9 + 2×3 + 9×3) = 2×(18 + 6 + 27) = 2×51 = 102 cm²

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#### 3rd Prism: 4m × 4m × 12m

Volume:
4 × 4 × 12 = 16 × 12 = 192 m³

Surface Area:
2×(4×4 + 4×12 + 4×12) = 2×(16 + 48 + 48) = 2×112 = 224 m²

*(Note: Two sides are same — it’s a long box with square ends)*

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#### 4th Prism: 70mm × 110mm × 20mm

Volume:
70 × 110 × 20
First: 70 × 110 = 7,700
Then: 7,700 × 20 = 154,000 mm³

Surface Area:
2×(70×110 + 70×20 + 110×20)
= 2×(7,700 + 1,400 + 2,200)
= 2×(11,300) = 22,600 mm²

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🔷 For Cubes:

All sides equal → let side = s

Formulas:
- Volume = s³
- Surface Area = 6 × s²

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#### 1st Cube: 6cm

Volume:
6³ = 6 × 6 × 6 = 36 × 6 = 216 cm³

Surface Area:
6 × (6²) = 6 × 36 = 216 cm²

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#### 2nd Cube: 30mm

Volume:
30³ = 30 × 30 × 30 = 900 × 30 = 27,000 mm³

Surface Area:
6 × (30²) = 6 × 900 = 5,400 mm²

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#### 3rd Cube: 8m

Volume:
8³ = 8 × 8 × 8 = 64 × 8 = 512 m³

Surface Area:
6 × (8²) = 6 × 64 = 384 m²

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#### 4th Cube: 5cm

Volume:
5³ = 5 × 5 × 5 = 25 × 5 = 125 cm³

Surface Area:
6 × (5²) = 6 × 25 = 150 cm²

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✔ All calculations double-checked!

Final Answer:

Rectangular Prisms:
1. Volume: 30 cm³, Surface Area: 62 cm²
2. Volume: 54 cm³, Surface Area: 102 cm²
3. Volume: 192 m³, Surface Area: 224 m²
4. Volume: 154000 mm³, Surface Area: 22600 mm²

Cubes:
1. Volume: 216 cm³, Surface Area: 216 cm²
2. Volume: 27000 mm³, Surface Area: 5400 mm²
3. Volume: 512 m³, Surface Area: 384 m²
4. Volume: 125 cm³, Surface Area: 150 cm²