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2 parts
a

9.0831 m29.0831 \text{ m}^2

8.9571 m28.9571 \text{ m}^2

b

0.1260 m20.1260 \text{ m}^2

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Part a· 3 steps

The maximum and minimum possible area of the floor

  1. Determine the limits of the length and width.

    The measured length (LL) is 4.1 m4.1 \text{ m} and the measured width (BB) is 2.2 m2.2 \text{ m}.
    The possible error in each measurement is 0.01 m0.01 \text{ m}.

    Thus, the limits for the length are:

    Lmin=4.1 m−0.01 m=4.09 mL_{min} = 4.1 \text{ m} - 0.01 \text{ m} = 4.09 \text{ m} Lmax=4.1 m+0.01 m=4.11 mL_{max} = 4.1 \text{ m} + 0.01 \text{ m} = 4.11 \text{ m}

    And the limits for the width are:

    Bmin=2.2 m−0.01 m=2.19 mB_{min} = 2.2 \text{ m} - 0.01 \text{ m} = 2.19 \text{ m} Bmax=2.2 m+0.01 m=2.21 mB_{max} = 2.2 \text{ m} + 0.01 \text{ m} = 2.21 \text{ m}
  2. Calculate the maximum possible area.

    The maximum area is found by multiplying the maximum possible length by the maximum possible width.

    Amax=Lmax×BmaxA_{max} = L_{max} \times B_{max} Amax=4.11 m×2.21 mA_{max} = 4.11 \text{ m} \times 2.21 \text{ m} Amax=9.0831 m2A_{max} = 9.0831 \text{ m}^2
  3. Calculate the minimum possible area.

    The minimum area is found by multiplying the minimum possible length by the minimum possible width.

    Amin=Lmin×BminA_{min} = L_{min} \times B_{min} Amin=4.09 m×2.19 mA_{min} = 4.09 \text{ m} \times 2.19 \text{ m} Amin=8.9571 m2A_{min} = 8.9571 \text{ m}^2

    The maximum possible area is 9.0831 m2\boxed{9.0831 \text{ m}^2} and the minimum possible area is 8.9571 m2\boxed{8.9571 \text{ m}^2}.

Part b

0.1260 m20.1260 \text{ m}^2

The maximum possible wastage in a carpet ordered to cover the entire floor

  1. Calculate the maximum possible wastage.

    To ensure the carpet covers the entire floor, the carpet will be ordered based on the maximum possible area of the floor (AmaxA_{max}).
    Maximum wastage occurs when the actual floor area is at its minimum (AminA_{min}).
    Maximum wastage = Area of carpet ordered - Minimum possible floor area

    Wastagemax=Amax−AminWastage_{max} = A_{max} - A_{min} Wastagemax=9.0831 m2−8.9571 m2Wastage_{max} = 9.0831 \text{ m}^2 - 8.9571 \text{ m}^2 Wastagemax=0.1260 m2Wastage_{max} = 0.1260 \text{ m}^2

    The maximum possible wastage is 0.1260 m2\boxed{0.1260 \text{ m}^2}.

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