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Previous Lesson

Surface Area of Solids

Geometry and Measures Surface Area of Solids

🎬 Video Tutorial

(0:01) Surface Area of a Cuboid: Calculate each pair of faces (top-bottom, front-back, left-right) and sum their areas to find the total surface area.
(1:00) Surface Area of a Cube: Since all 6 faces of a cube are identical squares, the surface area formula is $6 \times \text{side}^2$.
(2:21) Surface Area of a Triangular Prism: Add the areas of the two triangular faces and three rectangular faces.
Real-World Application: Knowing surface area is essential for practical tasks like painting or covering surfaces.

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📂 Revision Cards

Surface area calculation of a cuboid with labelled dimensions: length (l), width (w), and height (h). Illustration highlights 6 faces in 3 pairs. — 1) Surface Area of Solids

Illustration showing surface area formulas for a cuboid and a cube. The cuboid formula is 2lw + 2lh + 2hw, and the cube formula is 6a². — 2) Surface Area of Cuboids and Cubes

Diagram illustrating how to find the surface area of a cuboid with dimensions, by breaking down the calculations for each face and sum up. — 3) Calculating Surface Area of a Cuboid

A trapezoidal prism with labelled dimensions used to calculate its surface area. The faces include front and back triangles, base, top, and side. — 4) Calculting the surface area of a Prism

🍪 Quiz

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Surface Area of Solids

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Q: What is the surface area of a cube with a side length of 4 cm?

$48 \ \text{cm}^2$

$64 \ \text{cm}^2$

$96 \ \text{cm}^2$

$24 \ \text{cm}^2$

Feedback: Not quite! The surface area of a cube is 6 × (side length)². For a side length of 4 cm: 6 × (4 × 4) = 6 × 16 = 96 cm².

Feedback: Well done! The surface area of a cube is 6 × (side length)². For a side length of 4 cm: 6 × (4 × 4) = 6 × 16 = 96 cm².

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Q: What is the area of its top face?

$An cuboid with dimensions 6 m length, 3 m height, and 2 m width, with the top face highlighted.$

$10 \ \text{cm}^2$

$12 \ \text{cm}^2$

$15 \ \text{cm}^2$

$8 \ \text{cm}^2$

Feedback: Not quite! The area of the top face is calculated as length × width. For this cuboid: 6 m × 2 m = 12 m².

Feedback: Well done! The area of the top face is calculated as length × width. For this cuboid: 6 m × 2 m = 12 m².

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Q: A cube has a surface area of $150 \text{cm}^2$. What is the length of one side?

5 cm

7 cm

6 cm

8 cm

Feedback: Not quite! The surface area of a cube is 6 × (side length)². To find the side length: divide 150 cm² by 6 to get 25, then take the square root: $\sqrt{25}$ = 5 cm.

Feedback: Well done! The surface area of a cube is 6 × (side length)². To find the side length: divide 150 cm² by 6 to get 25, then take the square root: $\sqrt{25}$ = 5 cm.

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Q: A cuboid has a length of 12 cm, a width of 7 cm, and a height of 5 cm. What is its total surface area?

$394 \ \text{cm}^2$

$358 \ \text{cm}^2$

$372 \ \text{cm}^2$

$346 \ \text{cm}^2$

Feedback: Not quite! The total surface area of a cuboid is 2 × (length × width + length × height + width × height). For this cuboid: 2 × (12 × 7 + 12 × 5 + 7 × 5) = 2 × (84 + 60 + 35) = 2 × 179 = 358 cm².

Feedback: Well done! The total surface area of a cuboid is 2 × (length × width + length × height + width × height). For this cuboid: 2 × (12 × 7 + 12 × 5 + 7 × 5) = 2 × (84 + 60 + 35) = 2 × 179 = 358 cm².

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Q: A cuboid has a length of 15 cm, a width of 10 cm, and a height of 8 cm. What is its total surface area?

$700 \ \text{cm}^2$

$680 \ \text{cm}^2$

$740 \ \text{cm}^2$

$720 \ \text{cm}^2$

Feedback: Not quite! The total surface area of a cuboid is 2 × (length × width + length × height + width × height). For this cuboid: 2 × (15 × 10 + 15 × 8 + 10 × 8) = 2 × (150 + 120 + 80) = 2 × 350 = 700 cm².

Feedback: Well done! The total surface area of a cuboid is 2 × (length × width + length × height + width × height). For this cuboid: 2 × (15 × 10 + 15 × 8 + 10 × 8) = 2 × (150 + 120 + 80) = 2 × 350 = 700 cm².

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Q: Consider the cuboid below. Excluding its top face, what is its surface area?

$A cuboid with dimensions 12 m length, 8 m height, and 6 m width, with the top face highlighted.$

$336 \ \text{cm}^2$

$360 \ \text{cm}^2$

$340\ \text{cm}^2$

$384 \ \text{cm}^2$

Feedback: Not quite! Total surface area = 2 × (12 × 6 + 12 × 8 + 6 × 8) = 2 × (72 + 96 + 48) = 2 × 216 = 432 m². Excluding the top face: 432 - (12 × 6) = 432 - 72 = 360 m².

Feedback: Well done! Total surface area = 2 × (12 × 6 + 12 × 8 + 6 × 8) = 2 × (72 + 96 + 48) = 2 × 216 = 432 m². Excluding the top face: 432 - (12 × 6) = 432 - 72 = 360 m².

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