Let's solve the problem step by step.
We are asked to find the
surface area of a cube for each of the five cubes given. The formula for the
surface area (SA) of a cube is:
$$
\text{Surface Area} = 6 \times (\text{side length})^2
$$
This is because a cube has 6 equal square faces, and the area of one face is $ s^2 $, so total surface area is $ 6s^2 $.
---
🔷 Problem 1:
- Side length =
15 cm
$$
\text{SA} = 6 \times (15)^2 = 6 \times 225 = 1350 \text{ cm}^2
$$
✔ Answer: 1350 cm²
---
🔷 Problem 2:
- Side length =
2½ ft
Convert to improper fraction: $ 2\frac{1}{2} = \frac{5}{2} $ ft
$$
\text{SA} = 6 \times \left(\frac{5}{2}\right)^2 = 6 \times \frac{25}{4} = \frac{150}{4} = 37.5 \text{ ft}^2
$$
✔ Answer: 37.5 ft²
---
🔷 Problem 3:
- Side length =
0.6 m
$$
\text{SA} = 6 \times (0.6)^2 = 6 \times 0.36 = 2.16 \text{ m}^2
$$
✔ Answer: 2.16 m²
---
🔷 Problem 4:
- Side length =
3.2 cm
$$
\text{SA} = 6 \times (3.2)^2 = 6 \times 10.24 = 61.44 \text{ cm}^2
$$
✔ Answer: 61.44 cm²
---
🔷 Problem 5:
- Side length =
3¼ in
Convert to improper fraction: $ 3\frac{1}{4} = \frac{13}{4} $ in
$$
\text{SA} = 6 \times \left(\frac{13}{4}\right)^2 = 6 \times \frac{169}{16} = \frac{1014}{16} = 63.375 \text{ in}^2
$$
✔ Answer: 63.375 in²
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✔ Final Answers Table:
| CUBE | WORKING OUT | AREA |
|------|-------------|------|
| 1) | $ 6 \times 15^2 = 6 \times 225 = 1350 $ |
1350 cm² |
| 2) | $ 6 \times (2.5)^2 = 6 \times 6.25 = 37.5 $ |
37.5 ft² |
| 3) | $ 6 \times (0.6)^2 = 6 \times 0.36 = 2.16 $ |
2.16 m² |
| 4) | $ 6 \times (3.2)^2 = 6 \times 10.24 = 61.44 $ |
61.44 cm² |
| 5) | $ 6 \times (3.25)^2 = 6 \times 10.5625 = 63.375 $ |
63.375 in² |
> 💡 Note: For problem 5, $ 3\frac{1}{4} = 3.25 $, and $ 3.25^2 = 10.5625 $, then $ 6 \times 10.5625 = 63.375 $
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Parent Tip: Review the logic above to help your child master the concept of surface area cube worksheet.
