Volume and surface area of prisms Worked Solutions — GCSE Maths

Fully worked, step-by-step solutions to GCSE Volume and surface area of prisms questions. See exactly how to solve problems on volume of a cuboid, volume of a prism, cross-sectional area times length, cube.

volume of a cuboidvolume of a prismcross-sectional area times lengthcubesurface areanets
GCSE Foundation70 questionsStep-by-step solutions
Question 1
2 markseasy
A cuboid has length 33 cm, width 44 cm and height 55 cm. Work out the volume of the cuboid.

Worked solution

  1. Recall the rule for the volume of a cuboid.

    V=length×width×heightV = \text{length} \times \text{width} \times \text{height}

    A cuboid is a prism with a rectangular cross-section, so its volume is the three edge lengths multiplied together.

  2. Substitute the three edge lengths.

    V=3×4×5V = 3 \times 4 \times 5

    The edges are 33 cm, 44 cm and 55 cm.

  3. State the volume of the cuboid.

    V=60 cm3V = 60\text{ cm}^3

    The volume of the cuboid is 6060 cm3\text{cm}^3.

Answer
V=60 cm3V = 60\text{ cm}^3
Question 2
2 markseasy
A cuboid has length 66 cm, width 55 cm and height 22 cm. Work out the volume of the cuboid.

Worked solution

  1. Recall the rule for the volume of a cuboid.

    V=length×width×heightV = \text{length} \times \text{width} \times \text{height}

    A cuboid is a prism with a rectangular cross-section, so its volume is the three edge lengths multiplied together.

  2. Substitute the three edge lengths.

    V=6×5×2V = 6 \times 5 \times 2

    The edges are 66 cm, 55 cm and 22 cm.

  3. State the volume of the cuboid.

    V=60 cm3V = 60\text{ cm}^3

    The volume of the cuboid is 6060 cm3\text{cm}^3.

Answer
V=60 cm3V = 60\text{ cm}^3
Question 3
2 markseasy
A cuboid has length 1010 cm, width 44 cm and height 33 cm. Work out the volume of the cuboid.

Worked solution

  1. Recall the rule for the volume of a cuboid.

    V=length×width×heightV = \text{length} \times \text{width} \times \text{height}

    A cuboid is a prism with a rectangular cross-section, so its volume is the three edge lengths multiplied together.

  2. Substitute the three edge lengths.

    V=10×4×3V = 10 \times 4 \times 3

    The edges are 1010 cm, 44 cm and 33 cm.

  3. State the volume of the cuboid.

    V=120 cm3V = 120\text{ cm}^3

    The volume of the cuboid is 120120 cm3\text{cm}^3.

Answer
V=120 cm3V = 120\text{ cm}^3
Question 4
1 markeasy
A cube has edges of length 44 cm. Work out the volume of the cube.

Worked solution

  1. Recall the rule for the volume of a cube.

    V=a×a×a=a3V = a \times a \times a = a^3

    Every edge of a cube is the same length, so the volume is that length cubed.

  2. Substitute the edge length.

    V=43=4×4×4V = 4^3 = 4 \times 4 \times 4

    Each edge is 44 cm.

  3. State the volume of the cube.

    V=64 cm3V = 64\text{ cm}^3

    The volume of the cube is 6464 cm3\text{cm}^3.

Answer
V=64 cm3V = 64\text{ cm}^3
Question 5
2 markseasy
A cube has edges of length 55 cm. Work out the volume of the cube.

Worked solution

  1. Recall the rule for the volume of a cube.

    V=a×a×a=a3V = a \times a \times a = a^3

    Every edge of a cube is the same length, so the volume is that length cubed.

  2. Substitute the edge length.

    V=53=5×5×5V = 5^3 = 5 \times 5 \times 5

    Each edge is 55 cm.

  3. State the volume of the cube.

    V=125 cm3V = 125\text{ cm}^3

    The volume of the cube is 125125 cm3\text{cm}^3.

Answer
V=125 cm3V = 125\text{ cm}^3

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