Math worksheet for calculating volume and surface area of cuboids and cubes.

Let’s solve each problem step by step.

We’ll start with the Rectangular Prisms (also called cuboids).

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Formula Reminder:

For a rectangular prism with length = l, width = w, height = h:

- Volume = l × w × h
- Surface Area = 2×(l×w + l×h + w×h)

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#### 1. Rectangular Prism: 2cm × 3cm × 5cm

- Volume = 2 × 3 × 5 = 30 cm³
- Surface Area = 2×(2×3 + 2×5 + 3×5) = 2×(6 + 10 + 15) = 2×31 = 62 cm²

✔ Check: 6+10+15=31 → ×2 = 62 ✔️

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#### 2. Rectangular Prism: 2cm × 9cm × 3cm

- Volume = 2 × 9 × 3 = 54 cm³
- Surface Area = 2×(2×9 + 2×3 + 9×3) = 2×(18 + 6 + 27) = 2×51 = 102 cm²

✔ Check: 18+6+27=51 → ×2 = 102 ✔️

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#### 3. Rectangular Prism: 4m × 4m × 12m

Note: Two sides are 4m — so it’s like a long box with square ends.

- Volume = 4 × 4 × 12 = 192 m³
- Surface Area = 2×(4×4 + 4×12 + 4×12) = 2×(16 + 48 + 48) = 2×112 = 224 m²

✔ Check: 16+48+48=112 → ×2 = 224 ✔️

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#### 4. Rectangular Prism: 70mm × 110mm × 20mm

- Volume = 70 × 110 × 20
First: 70 × 20 = 1400
Then: 1400 × 110 = 1400 × 100 + 1400 × 10 = 140,000 + 14,000 = 154,000 mm³

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

✔ Check: 7700+1400=9100; 9100+2200=11300 → ×2=22600 ✔️

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Now for the Cubes.

Formula for cube with side = s:

- Volume = s³ = s × s × s
- Surface Area = 6 × s² (since 6 faces, each is s×s)

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#### 5. Cube: 6cm

- Volume = 6 × 6 × 6 = 216 cm³
- Surface Area = 6 × (6×6) = 6 × 36 = 216 cm²

✔ Interesting — same number! But different units. ✔️

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#### 6. Cube: 30mm

- Volume = 30 × 30 × 30 = 900 × 30 = 27,000 mm³
- Surface Area = 6 × (30×30) = 6 × 900 = 5,400 mm²

✔ Check: 30²=900 → ×6=5400 ✔️

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#### 7. Cube: 8m

- Volume = 8 × 8 × 8 = 64 × 8 = 512 m³
- Surface Area = 6 × (8×8) = 6 × 64 = 384 m²

✔ Check: 8²=64 → ×6=384 ✔️

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#### 8. Cube: 5cm

- Volume = 5 × 5 × 5 = 125 cm³
- Surface Area = 6 × (5×5) = 6 × 25 = 150 cm²

✔ Check: 5²=25 → ×6=150 ✔️

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All calculations double-checked and correct.

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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: 154,000 mm³, Surface Area: 22,600 mm²

Cubes:

5. Volume: 216 cm³, Surface Area: 216 cm²
6. Volume: 27,000 mm³, Surface Area: 5,400 mm²
7. Volume: 512 m³, Surface Area: 384 m²
8. Volume: 125 cm³, Surface Area: 150 cm²