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Calculate the surface area and volume of a cuboid with length 5 cm, width 3 cm, and height 2 cm.

Mathematics

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2 parts
b

62 cm2\text{62 cm}^2

c

30 cm3\text{30 cm}^3

Step-by-step solution

6 steps

Here are the calculations for the surface area and volume of the cuboid.

Part b· 3 steps

Calculate the surface area of the cuboid.

  1. Identify the dimensions of the cuboid.

    Length (LL) = 5 cm
    Width (WW) = 3 cm
    Height (HH) = 2 cm

  2. Use the formula for the surface area of a cuboid.

    The surface area (SA) of a cuboid is given by the formula:

    SA=2(LW+LH+WH)SA = 2(LW + LH + WH)

  3. Substitute the dimensions into the formula and calculate.

    SA=2((5 cm×3 cm)+(5 cm×2 cm)+(3 cm×2 cm))SA = 2((5 \text{ cm} \times 3 \text{ cm}) + (5 \text{ cm} \times 2 \text{ cm}) + (3 \text{ cm} \times 2 \text{ cm})) SA=2(15 cm2+10 cm2+6 cm2)SA = 2(15 \text{ cm}^2 + 10 \text{ cm}^2 + 6 \text{ cm}^2) SA=2(31 cm2)SA = 2(31 \text{ cm}^2) SA=62 cm2SA = 62 \text{ cm}^2

    The student's calculation for the surface area is correct.
    The surface area of the cuboid is 62 cm2\boxed{\text{62 cm}^2}.

Part c

30 cm3\text{30 cm}^3

Calculate the volume of the solid.

  1. Identify the dimensions of the cuboid.

    Length (LL) = 5 cm
    Width (WW) = 3 cm
    Height (HH) = 2 cm

  2. Use the formula for the volume of a cuboid.

    The volume (V) of a cuboid is given by the formula:

    V=L×W×HV = L \times W \times H

  3. Substitute the dimensions into the formula and calculate.

    V=5 cm×3 cm×2 cmV = 5 \text{ cm} \times 3 \text{ cm} \times 2 \text{ cm} V=15 cm2×2 cmV = 15 \text{ cm}^2 \times 2 \text{ cm} V=30 cm3V = 30 \text{ cm}^3

    The student's calculation for the volume is correct.
    The volume of the solid is 30 cm3\boxed{\text{30 cm}^3}.

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