Surface area calculations for cuboids and cubes with step-by-step breakdown.

Let’s solve each problem step by step.

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Problem 1: Cuboid with dimensions 10 cm (length), 3 cm (width), 4 cm (height)

We need to find the area of each face and then total surface area.

- Front side: This is length × height = 10 cm × 4 cm = 40 cm²
- Back side: Same as front → 40 cm²
- Top side: This is length × width = 10 cm × 3 cm = 30 cm²
- Bottom side: Same as top → 30 cm²
- Right side: This is width × height = 3 cm × 4 cm = 12 cm²
- Left side: Same as right → 12 cm²

Now add them all up for total surface area:

40 + 40 + 30 + 30 + 12 + 12 =
→ 80 (front+back) + 60 (top+bottom) + 24 (right+left) = 164 cm²

✔ Check: Formula for cuboid surface area = 2(lw + lh + wh)
= 2(10×3 + 10×4 + 3×4) = 2(30 + 40 + 12) = 2(82) = 164 → Correct!

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Problem 2: Cuboid with dimensions 9 mm (length), 2 mm (width), 3 mm (height)

Same logic:

- Front side: length × height = 9 × 3 = 27 mm²
- Back side: same → 27 mm²
- Top side: length × width = 9 × 2 = 18 mm²
- Bottom side: same → 18 mm²
- Right side: width × height = 2 × 3 = 6 mm²
- Left side: same → 6 mm²

Total surface area:

27 + 27 + 18 + 18 + 6 + 6 =
→ 54 (front+back) + 36 (top+bottom) + 12 (right+left) = 102 mm²

✔ Check with formula: 2(lw + lh + wh) = 2(9×2 + 9×3 + 2×3) = 2(18 + 27 + 6) = 2(51) = 102 → Correct!

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Problem 3: Cube with side 7 cm

A cube has 6 identical square faces.

- Area of one square = side × side = 7 × 7 = 49 cm²
- Total surface area = 6 × area of one face = 6 × 49 = 294 cm²

✔ Check: Formula for cube surface area = 6s² = 6×49 = 294 → Correct!

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Final Answer:

1)
FRONT side = 40 cm²
BACK side = 40 cm²
TOP side = 30 cm²
BOTTOM side = 30 cm²
RIGHT side = 12 cm²
LEFT side = 12 cm²
Total surface area = 164 cm²

2)
FRONT side = 27 mm²
BACK side = 27 mm²
TOP side = 18 mm²
BOTTOM side = 18 mm²
RIGHT side = 6 mm²
LEFT side = 6 mm²
Total surface area = 102 mm²

3)
Area of one square = 49 cm²
Total surface area = 6 x 49 = 294 cm²