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Determine the area of the entire canvas in square centimetres.

Mathematics

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Answer

8253,3 cm28253,3 \text{ cm}^2

119

Step-by-step solution

6 steps

4.1.1

  1. Convert the width of the canvas from feet to centimetres.

    The width is given as 2,46 ft2,46 \text{ ft}.
    We are given the conversion factor 1 ft=30,5 cm1 \text{ ft} = 30,5 \text{ cm}.

    Width=2,46 ft×30,5cmft\text{Width} = 2,46 \text{ ft} \times 30,5 \frac{\text{cm}}{\text{ft}} Width=75,03 cm\text{Width} = 75,03 \text{ cm}
  2. Calculate the area of the canvas.

    The length of the canvas is 110 cm110 \text{ cm}.
    The formula for the area of a rectangle is Area=length×width\text{Area} = \text{length} \times \text{width}.

    Area=110 cm×75,03 cm\text{Area} = 110 \text{ cm} \times 75,03 \text{ cm} Area=8253,3 cm2\text{Area} = 8253,3 \text{ cm}^2

    The area of the entire canvas is 8253,3 cm2\boxed{8253,3 \text{ cm}^2}.

    4.1.2

  3. Interpret the question regarding the painted area.

    The question states that Nandipha "will paint the rest of the canvas" but then asks to "Calculate the total surface area that needs to be painted if she paints the overlap as well." Painting the "overlap as well" means that she applies paint to the entire canvas surface, including the areas that will later be covered by bottlecaps and plastic. Therefore, the total surface area to be painted is the entire area of the canvas.

  4. State the total surface area to be painted.

    From question 4.1.1, the area of the entire canvas is 8253,3 cm28253,3 \text{ cm}^2.
    The total surface area that needs to be painted is 8253,3 cm2\boxed{8253,3 \text{ cm}^2}.

    4.1.3

  5. Determine the number of bottlecaps for each circle.

    There are three circles. Let's denote them as C1 (largest), C2 (middle), and C3 (smallest).
    The largest circle (C1) takes 68 bottlecaps.
    The problem states that "each circle is half the size of the adjacent circle." Assuming "size" refers to the area covered by bottlecaps:
    Number of caps for C2 = 0,5×Number of caps for C10,5 \times \text{Number of caps for C1}

    Caps for C2=0,5×68=34\text{Caps for C2} = 0,5 \times 68 = 34

    Number of caps for C3 = 0,5×Number of caps for C20,5 \times \text{Number of caps for C2}

    Caps for C3=0,5×34=17\text{Caps for C3} = 0,5 \times 34 = 17
  6. Calculate the total number of bottlecaps needed.

    Add the number of caps for all three circles.

    Total caps=Caps for C1+Caps for C2+Caps for C3\text{Total caps} = \text{Caps for C1} + \text{Caps for C2} + \text{Caps for C3} Total caps=68+34+17\text{Total caps} = 68 + 34 + 17 Total caps=119\text{Total caps} = 119

    The approximate amount of bottle caps Nandipha will need is 119\boxed{119}.

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