Let's solve each problem step by step. All the figures shown are
nets of cubes, meaning they represent the 6 faces of a cube unfolded into a flat shape.
Key Concept:
- A cube has
6 equal square faces.
- The
surface area (SA) of a cube is:
$$
\text{SA} = 6 \times (\text{side length})^2
$$
- Each face is a square, so if the side length is $ s $, then one face has area $ s^2 $, and total surface area is $ 6s^2 $.
---
We'll go through each question:
---
1)
- Given: Width = 7 cm
- Find: Surface area
$$
\text{SA} = 6 \times (7)^2 = 6 \times 49 = 294 \text{ cm}^2
$$
✔ Answer: 294 cm²
---
2)
- Given: Surface area = 24 in²
- Find: Width (side length)
Use:
$$
6s^2 = 24 \\
s^2 = \frac{24}{6} = 4 \\
s = \sqrt{4} = 2 \text{ in}
$$
✔ Answer: Width = 2 in
---
3)
- Given: Width = 11 cm
- Find: Surface area
$$
\text{SA} = 6 \times (11)^2 = 6 \times 121 = 726 \text{ cm}^2
$$
✔ Answer: 726 cm²
---
4)
- Given: Surface area = 600 ft²
- Find: Width
$$
6s^2 = 600 \\
s^2 = 100 \\
s = \sqrt{100} = 10 \text{ ft}
$$
✔ Answer: Width = 10 ft
---
5)
- Given: Width = $ 3\frac{1}{4} $ m = $ 3.25 $ m
- Find: Surface area
Convert to fraction: $ 3\frac{1}{4} = \frac{13}{4} $
$$
s^2 = \left(\frac{13}{4}\right)^2 = \frac{169}{16} \\
\text{SA} = 6 \times \frac{169}{16} = \frac{1014}{16} = 63.375 \text{ m}^2
$$
Or as a mixed number:
$ 63.375 = 63 \frac{3}{8} $ m²
✔ Answer: 63.375 m² or $ 63\frac{3}{8} $ m²
---
6)
- Given: Surface area = 150 in²
- Find: Width
$$
6s^2 = 150 \\
s^2 = 25 \\
s = \sqrt{25} = 5 \text{ in}
$$
✔ Answer: Width = 5 in
---
7)
- Given: Width = 30 cm
- Find: Surface area
$$
\text{SA} = 6 \times (30)^2 = 6 \times 900 = 5400 \text{ cm}^2
$$
✔ Answer: 5400 cm²
---
8)
- Given: Surface area = 216 in²
- Find: Width
$$
6s^2 = 216 \\
s^2 = 36 \\
s = \sqrt{36} = 6 \text{ in}
$$
✔ Answer: Width = 6 in
---
✔ Final Answers:
| Question | Answer |
|--------|--------|
| 1) | 294 cm² |
| 2) | 2 in |
| 3) | 726 cm² |
| 4) | 10 ft |
| 5) | 63.375 m² or $ 63\frac{3}{8} $ m² |
| 6) | 5 in |
| 7) | 5400 cm² |
| 8) | 6 in |
---
🔍 Summary:
All problems use the formula for surface area of a cube:
$$
\boxed{\text{SA} = 6s^2}
$$
You either plug in $ s $ to find SA, or use SA to solve for $ s $.
Let me know if you'd like this printed out or formatted for a worksheet!
Parent Tip: Review the logic above to help your child master the concept of surface area of a cube worksheet.
