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Maths · Geometry & Measures

Volume & surface area of cuboids

Compute volume and surface area of rectangular prisms.

Not startedCAMBRIDGE · 8CBSE · VIIIIB · MYP-2

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What is a cuboid?

A cuboid is a 3D shape with six rectangular faces. Think of a shoebox or a brick. It has three dimensions: length, width and height. All the corners meet at right angles.

Finding the volume

Volume measures the space inside a 3D shape. For a cuboid, multiply length × width × height. We measure volume in cubic units like cm³ or m³. The formula is V = l × w × h.

Finding the surface area

Surface area is the total area of all six faces. A cuboid has three pairs of identical rectangles. The formula is SA = 2lw + 2lh + 2wh. Measure surface area in square units like cm² or m².

Why these formulas work

Volume counts how many unit cubes fit inside. Surface area adds the area of each face. Opposite faces are identical, so we calculate three different rectangles and double each one.

Worked examples

  1. 1. Find the volume of a cuboid with length 5 cm, width 3 cm and height 4 cm.

    1. Use the formula V = l × w × h
    2. Substitute the values: V = 5 × 3 × 4
    3. Calculate: V = 60 cm³

  2. 2. Find the surface area of a cuboid with length 6 m, width 2 m and height 3 m.

    1. Use the formula SA = 2lw + 2lh + 2wh
    2. Substitute: SA = 2(6×2) + 2(6×3) + 2(2×3)
    3. Calculate: SA = 2(12) + 2(18) + 2(6) = 24 + 36 + 12
    4. Total surface area = 72 m²

  3. 3. A cuboid has volume 120 cm³, length 8 cm and width 3 cm. Find the height.

    1. Start with V = l × w × h, so 120 = 8 × 3 × h
    2. Simplify: 120 = 24 × h
    3. Divide both sides by 24: h = 120 ÷ 24 = 5 cm

Try it yourself

A cuboid has length 10 cm, width 4 cm and height 2 cm. What is its volume?

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