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Determine the diameter of a hockey ball.

Mathematics

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1.3.1

  1. Determine the diameter of a hockey ball.

    The radius of a hockey ball is 35.5 mm35.5 \text{ mm}.
    The diameter of a hockey ball is Dball=2×35.5 mm=71 mmD_{ball} = 2 \times 35.5 \text{ mm} = 71 \text{ mm}.

  2. Determine how many hockey balls can fit across the diameter of Container A.

    The diameter of Container A is 73 mm73 \text{ mm}.
    Number of balls across diameter = Container A diameterHockey ball diameter=73 mm71 mm≈1.02\frac{\text{Container A diameter}}{\text{Hockey ball diameter}} = \frac{73 \text{ mm}}{71 \text{ mm}} \approx 1.02.
    Since only whole balls can fit, 1 hockey ball can fit across the diameter.

  3. Determine how many hockey balls can fit along the height of Container A.

    The height of Container A is 280 mm280 \text{ mm}.
    Number of balls along height = Container A heightHockey ball diameter=280 mm71 mm≈3.94\frac{\text{Container A height}}{\text{Hockey ball diameter}} = \frac{280 \text{ mm}}{71 \text{ mm}} \approx 3.94.
    Since only whole balls can fit, 3 hockey balls can fit along the height.

  4. Calculate the total number of hockey balls that can fit into Container A.

    Total balls = (balls across diameter) ×\times (balls along height)
    Total balls = 1×3=31 \times 3 = 3
    Thus, 3 hockey balls\boxed{\text{3 hockey balls}} can fit into CONTAINER A.

    1.3.2

  5. Determine the diameter of a hockey ball.

    The diameter of a hockey ball is 71 mm71 \text{ mm} (from 1.3.1).

  6. Convert all dimensions of Container B to millimeters.

    Length = 240 mm240 \text{ mm}.
    Width = 17 cm=17×10 mm=170 mm17 \text{ cm} = 17 \times 10 \text{ mm} = 170 \text{ mm}.
    Height = 100 mm100 \text{ mm}.

  7. Determine how many hockey balls can fit along each dimension of Container B.

    Number of balls along length = 240 mm71 mm≈3.38\frac{240 \text{ mm}}{71 \text{ mm}} \approx 3.38. So, 3 balls.
    Number of balls along width = 170 mm71 mm≈2.39\frac{170 \text{ mm}}{71 \text{ mm}} \approx 2.39. So, 2 balls.
    Number of balls along height = 100 mm71 mm≈1.40\frac{100 \text{ mm}}{71 \text{ mm}} \approx 1.40. So, 1 ball.

  8. Calculate the total number of hockey balls that can fit into Container B.

    Total balls = (balls along length) ×\times (balls along width) ×\times (balls along height)
    Total balls = 3×2×1=63 \times 2 \times 1 = 6
    Thus, 6 hockey balls\boxed{\text{6 hockey balls}} can fit into CONTAINER B.

    1.3.3

    Container A is a cylindrical shape, which is a better match for the spherical hockey balls. This allows for a more snug fit, minimizing wasted space and preventing the balls from moving around and potentially getting damaged during transport.

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