Andy is making paper boxes of different sizes. The supplies are limited; therefore, Andy restricted the volume of each box to 240 cubic inch

Question

Andy is making paper boxes of different sizes. The supplies are limited; therefore, Andy restricted the volume of each box to 240 cubic inches or less and the base area to exactly 30 square inches. Find the range of the height, h.

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Amaya 2 weeks 2021-09-13T03:29:35+00:00 1 Answer 0

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    2021-09-13T03:31:12+00:00

    Answer:

    The range of the height of the box is 1 inch to 8 inches

    Step-by-step explanation:

    Given

    Volume of a rectangular box = 240 cubic inches (or less)

    Base area of each box = 30 square inches

    Required

    The range of the height of the box

    To calculate the range of the height, we need to get the minimum and maximum height.

    Calculating the maximum height

    This is attained when the volume of the rectangular box is 240 cubic inches

    The volume of a rectangular box is calculated thus

    Volume = Base Area * Height

    Substituting 240 for volume and 30 for base area; this gives

    240 = 30 * Height

    Divide both sides by 30

    \frac{240}{30} = \frac{30 * Height}{30}

    8 = Height

    Height  = 8 inches

    Hence, the maximum height is 8 inches

    Calculating the minimum height

    The minimum height is attained when the base area equals the volume.

    In other words,

    When volume = 30 cubic inches and base area = 30 square inches

    Recall that

    Volume = Base Area * Height

    Substituting 30 for volume and 30 for base area; this gives

    30 = 30 * Height

    Divide both sides by 30

    \frac{30}{30} = \frac{30 * Height}{30}

    1 = Height

    Height  = 1 inch

    Hence, the minimum height is 1 inch

    The range of the height of the box is 1 inch to 8 inches

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