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A round tablecloth needs to cover a table with a diameter of 1.6 m. If an additional 20 cm of fabric is needed all around the edge, what is the new diameter and area of the tablecloth?

Mathematics

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1.2.1 Determine the new diameter of the tablecloth in metres.

  1. Identify the original diameter and the extra fabric added.

    The original diameter of the table is 1.6 m1.6 \text{ m}.
    The extra fabric added all around the edge is 20 cm20 \text{ cm}.

  2. Convert the extra fabric measurement to metres.

    20 cm=20100 m=0.2 m20 \text{ cm} = \frac{20}{100} \text{ m} = 0.2 \text{ m}
  3. Calculate the total increase in diameter.

    Since the extra fabric is added all around the edge, it adds to the radius on both sides. Therefore, the diameter increases by twice the extra fabric amount.
    Total increase in diameter =2×0.2 m=0.4 m= 2 \times 0.2 \text{ m} = 0.4 \text{ m}

  4. Calculate the new diameter of the tablecloth.

    New diameter = Original diameter + Total increase in diameter

    New diameter=1.6 m+0.4 m=2.0 m\text{New diameter} = 1.6 \text{ m} + 0.4 \text{ m} = 2.0 \text{ m}

    The new diameter of the tablecloth is 2.0 m\boxed{\text{2.0 m}}.

    1.2.2 Calculate the area of fabric required for ONE tablecloth in square metres.

  5. Determine the radius of the new tablecloth.

    The new diameter is 2.0 m2.0 \text{ m}.
    Radius r=Diameter2=2.0 m2=1.0 mr = \frac{\text{Diameter}}{2} = \frac{2.0 \text{ m}}{2} = 1.0 \text{ m}

  6. Calculate the area of the fabric using the formula A=πr2A = \pi r^2.

    A=π(1.0 m)2A = \pi (1.0 \text{ m})^2 A=π×1.0 m2A = \pi \times 1.0 \text{ m}^2 A=π m2A = \pi \text{ m}^2

    Using π≈3.14159\pi \approx 3.14159:

    A≈3.14159 m2A \approx 3.14159 \text{ m}^2

    The area of fabric required for one tablecloth is approximately 3.14 m2\boxed{\text{3.14 m}^2}.

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