Math

Hank has cards that are 8 inches by 4 inches. A stack of these cards fit inside the box shown and uses up 32 inches of volume. How tall is the stack of cards? What percent of the box's volume is taken up by the cards?

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  1. Ab = Area of base = 8 ∙ 4 = 32 in²

    Vc = Volume of cards = Ab ∙ h = 32 in³

    Ab ∙ h = 32 in³

    32 in² ∙ h = 32 in³

    h = 32 in³ / 32 in² = 1 in

    Card stack is 1 inch high.

    Volume of box:

    Vb = 8 ∙ 4 ∙ 4 =128 in³

    32 in³ of cards taken:

    ( Vc / Vb ) ∙ 100% = ( 32 / 128 ) ∙ 100% = 0.25 ∙ 100% = 25%

    25% the box's volume is taken up by the cards.

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