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A box measuring 28 cm by 15 cm by 8 cm is packed with 84 rectangular chocolate bars. If the base of each chocolate bar has an area of 35 cm², what is the thickness of one chocolate bar?

Mathematics

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24.1.1

  1. Identify the dimensions of the box.

    The length of the box is L=28 cmL = 28 \text{ cm}.
    The width of the box is W=15 cmW = 15 \text{ cm}.
    The height of the box is H=8 cmH = 8 \text{ cm}.

  2. Use the formula for the volume of a rectangular prism.

    V=L×W×HV = L \times W \times H

  3. Substitute the values and calculate the volume.

    V=28 cm×15 cm×8 cmV = 28 \text{ cm} \times 15 \text{ cm} \times 8 \text{ cm} V=420 cm2×8 cmV = 420 \text{ cm}^2 \times 8 \text{ cm} V=3360 cm3V = 3360 \text{ cm}^3

    The volume of the box is 3360 cm3\boxed{\text{3360 cm}^3}.

    24.1.2

  4. Calculate the volume of one chocolate bar.

    The box packs 84 rectangular chocolate bars. The total volume of the chocolate bars is the volume of the box.

    Vchocolate=Volume of boxNumber of chocolate barsV_{\text{chocolate}} = \frac{\text{Volume of box}}{\text{Number of chocolate bars}} Vchocolate=3360 cm384V_{\text{chocolate}} = \frac{3360 \text{ cm}^3}{84} Vchocolate=40 cm3V_{\text{chocolate}} = 40 \text{ cm}^3

  5. Identify the given area of the base of a chocolate bar.

    Area of base = 35 cm235 \text{ cm}^2.

  6. Use the formula Volume = area of base ×\times thickness to find the thickness.

    Vchocolate=Area of base×thicknessV_{\text{chocolate}} = \text{Area of base} \times \text{thickness} 40 cm3=35 cm2×thickness40 \text{ cm}^3 = 35 \text{ cm}^2 \times \text{thickness} thickness=40 cm335 cm2\text{thickness} = \frac{40 \text{ cm}^3}{35 \text{ cm}^2} thickness=87 cm\text{thickness} = \frac{8}{7} \text{ cm} thickness≈1.14 cm\text{thickness} \approx 1.14 \text{ cm}

    The thickness of a chocolate bar is 87 cm≈1.14 cm\boxed{\frac{8}{7} \text{ cm} \approx 1.14 \text{ cm}}.

    24.2
    This question asks about the dimensions for a circular tablecloth and the available square material. I will calculate the required diameter of the tablecloth.

  7. Identify the diameter of the table.

    Diameter of table = 130 cm130 \text{ cm}.

  8. Calculate the diameter of the tablecloth needed to cover the table and hang over.

    The tablecloth hangs 25 cm25 \text{ cm} over the edge on all sides.

    Dno hem=Diameter of table+2×OverhangD_{\text{no hem}} = \text{Diameter of table} + 2 \times \text{Overhang} Dno hem=130 cm+2×25 cmD_{\text{no hem}} = 130 \text{ cm} + 2 \times 25 \text{ cm} Dno hem=130 cm+50 cmD_{\text{no hem}} = 130 \text{ cm} + 50 \text{ cm} Dno hem=180 cmD_{\text{no hem}} = 180 \text{ cm}

  9. Calculate the total diameter of the tablecloth needed, including the hem.

    A hem of 1.8 cm1.8 \text{ cm} is added right around. This means 1.8 cm1.8 \text{ cm} is added to the radius on all sides, so 2×1.8 cm2 \times 1.8 \text{ cm} is added to the diameter.

    Drequired=Dno hem+2×Hem allowanceD_{\text{required}} = D_{\text{no hem}} + 2 \times \text{Hem allowance} Drequired=180 cm+2×1.8 cmD_{\text{required}} = 180 \text{ cm} + 2 \times 1.8 \text{ cm} Drequired=180 cm+3.6 cmD_{\text{required}} = 180 \text{ cm} + 3.6 \text{ cm} Drequired=183.6 cmD_{\text{required}} = 183.6 \text{ cm}

  10. State the dimensions of the available material.

    The tablecloth material is square with a side length of 2.3 m2.3 \text{ m}.
    Convert meters to centimeters:
    Side length of material = 2.3 m×100 cm/m=230 cm2.3 \text{ m} \times 100 \text{ cm/m} = 230 \text{ cm}.

    The required diameter for the circular tablecloth is 183.6 cm\boxed{\text{183.6 cm}}. The available square material has a side length of 230 cm\boxed{\text{230 cm}}.

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