Surface Area: Cube/Cuboid Textbook Exercise - Corbettmaths - Free Printable

Let's solve the problems step by step.

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🔷 Surface Area of Cubes and Cuboids

We will use these formulas:

- Cube: All sides are equal.
Surface Area = $ 6 \times (\text{side})^2 $

- Cuboid: Three different dimensions: length (l), width (w), height (h)
Surface Area = $ 2(lw + lh + wh) $

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## ✔ Question 1: Surface Area of Cubes

(a) Cube with side = 2 cm

$$
\text{Surface Area} = 6 \times (2)^2 = 6 \times 4 = 24 \text{ cm}^2
$$

✔ Answer: 24 cm²

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(b) Cube with side = 5 cm

$$
\text{Surface Area} = 6 \times (5)^2 = 6 \times 25 = 150 \text{ cm}^2
$$

✔ Answer: 150 cm²

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(c) Cube with side = 7 mm

$$
\text{Surface Area} = 6 \times (7)^2 = 6 \times 49 = 294 \text{ mm}^2
$$

✔ Answer: 294 mm²

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## ✔ Question 2: Surface Area of Cuboids

Use formula:
$$
\text{SA} = 2(lw + lh + wh)
$$

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(a) Dimensions: 5 cm × 4 cm × 2 cm

Let’s assign:
- l = 5 cm
- w = 4 cm
- h = 2 cm

$$
\text{SA} = 2(5 \times 4 + 5 \times 2 + 4 \times 2) = 2(20 + 10 + 8) = 2 \times 38 = 76 \text{ cm}^2
$$

✔ Answer: 76 cm²

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(b) Dimensions: 10 cm × 3 cm × 1 cm

Let’s assign:
- l = 10 cm
- w = 3 cm
- h = 1 cm

$$
\text{SA} = 2(10 \times 3 + 10 \times 1 + 3 \times 1) = 2(30 + 10 + 3) = 2 \times 43 = 86 \text{ cm}^2
$$

✔ Answer: 86 cm²

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(c) Dimensions: 20 cm × 3 cm × 15 cm

Let’s assign:
- l = 20 cm
- w = 3 cm
- h = 15 cm

$$
\text{SA} = 2(20 \times 3 + 20 \times 15 + 3 \times 15) = 2(60 + 300 + 45) = 2 \times 405 = 810 \text{ cm}^2
$$

✔ Answer: 810 cm²

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## ✔ Final Answers:

Question 1:

- (a) 24 cm²
- (b) 150 cm²
- (c) 294 mm²

Question 2:

- (a) 76 cm²
- (b) 86 cm²
- (c) 810 cm²

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