Surface Area - Digital and Printable - Free Printable

Actually, there are several errors in the provided answers on the worksheet. Let’s go through each problem one by one, correct the mistakes, and explain the proper method for calculating surface area.

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## 🔷 Problem 1: Cube with side = 3 cm

✔ Correct Answer: 54 cm²

- Each face is a square: 3 cm × 3 cm = 9 cm²
- A cube has 6 identical faces → 6 × 9 = 54 cm²
- ✔ This one is correct.

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## 🔷 Problem 2: Cube with side = 4 cm

✔ Correct Answer: 96 cm²

- Each face: 4 cm × 4 cm = 16 cm²
- 6 faces → 6 × 16 = 96 cm²
- ✔ This one is also correct.

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## 🔷 Problem 3: Rectangular Prism (2 ft × 2 ft × 6 ft)

✘ Incorrect Answer: 56 cm² — Units are wrong! Should be ft², not cm².

Also, let’s recalculate:

This is a rectangular prism with dimensions:
- Length = 2 ft
- Width = 2 ft
- Height = 6 ft

It has 6 faces:
- Top & Bottom: 2 ft × 2 ft = 4 ft² → 2 faces → 2 × 4 = 8 ft²
- Front & Back: 2 ft × 6 ft = 12 ft² → 2 faces → 2 × 12 = 24 ft²
- Left & Right: 2 ft × 6 ft = 12 ft² → 2 faces → 2 × 12 = 24 ft²

✔ Total Surface Area = 8 + 24 + 24 = 56 ft²

➡️ So the numerical value is correct (56), but units are wrong — it should be ft², not cm².

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## 🔷 Problem 4: Rectangular Prism (5 m × 3 m × 10 m)

✘ Incorrect Answer: 190 cm² — Again, units are wrong! Should be m², not cm².

Let’s calculate correctly:

Dimensions:
- Length = 5 m
- Width = 3 m
- Height = 10 m

Faces:
- Top & Bottom: 5 m × 3 m = 15 m² → 2 faces → 2 × 15 = 30 m²
- Front & Back: 5 m × 10 m = 50 m² → 2 faces → 2 × 50 = 100 m²
- Left & Right: 3 m × 10 m = 30 m² → 2 faces → 2 × 30 = 60 m²

✔ Total Surface Area = 30 + 100 + 60 = 190 m²

➡️ Numerical value is correct, but units are wrong — should be m², not cm².

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## 🔷 Problem 5: Square Pyramid (Base 8 ft × 8 ft, Slant Height 10 ft?)

✘ Incorrect Answer: 224 cm² — Units wrong again! Should be ft², not cm².

Also, the calculation is flawed.

Let’s analyze:

- Base: 8 ft × 8 ft = 64 ft²
- Lateral Faces: 4 triangular faces.

Each triangle has:
- Base = 8 ft
- Height (slant height) = 10 ft (as labeled on diagram)

Area of one triangle = (1/2) × base × height = (1/2) × 8 × 10 = 40 ft²

→ 4 triangles = 4 × 40 = 160 ft²

✔ Total Surface Area = Base + Lateral Faces = 64 + 160 = 224 ft²

➡️ So the numerical value is correct (224), but units are wrong — should be ft², not cm².

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## 🚫 Summary of Errors:

| Problem | Numerical Value | Units | Verdict |
|---------|------------------|-------|---------|
| 1 | 54 | cm² | ✔ Correct |
| 2 | 96 | cm² | ✔ Correct |
| 3 | 56 | cm² ✘ | ✘ Wrong unit (should be ft²) |
| 4 | 190 | cm² ✘ | ✘ Wrong unit (should be m²) |
| 5 | 224 | cm² ✘ | ✘ Wrong unit (should be ft²) |

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## ✔ Final Correct Answers:

1. 54 cm²
2. 96 cm²
3. 56 ft²
4. 190 m²
5. 224 ft²

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## 💡 Key Takeaway:

> Always match the units in your answer to the units given in the problem! Mixing cm, m, and ft leads to incorrect answers even if the number is right.

Also, remember:
- Cube: SA = 6 × (side)²
- Rectangular Prism: SA = 2(lw + lh + wh)
- Square Pyramid: SA = Base Area + 4 × (½ × base × slant height)

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Let me know if you’d like a printable corrected version or step-by-step diagrams!