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?
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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To find the height of the stack of cards, we need to know the volume of each card. The volume of a rectangular prism can be calculated by multiplying its length, width, and height. In this case, the length and width of the card are given as 8 inches and 4 inches respectively. However, the height of the card is missing. Let's represent the height of the card as 'h'.
The volume of the card can be calculated as:
Volume of card = length × width × height = 8 inches × 4 inches × h = 32h cubic inches.
Given that a stack of these cards uses up 32 cubic inches of volume, we can set up the following equation:
32h = 32.
Simplifying the equation, we have:
h = 32/32 = 1 inch.
Therefore, the height of the stack of cards is 1 inch.
To find the percentage of the box's volume taken up by the cards, we need to calculate the ratio of the volume of the cards to the volume of the box.
The volume of the box is not provided. If you can provide the dimensions of the box or any additional information, we can calculate the percentage by comparing the volume of the cards to the volume of the box.
To find the height of the stack of cards, you need to divide the volume of the stack by the base area of one card.
First, calculate the base area of one card by multiplying the length and width:
Base area of one card = 8 inches x 4 inches = 32 square inches.
Next, divide the total volume of the stack by the base area of one card. We are given that the stack uses up 32 inches of volume. Therefore, the height of the stack can be calculated as follows:
Height of the stack = Total volume of stack / Base area of one card
Height of the stack = 32 inches / 32 square inches = 1 inch
So, the stack of cards is 1 inch tall.
Now, let's find the percentage of the box's volume occupied by the cards.
First, calculate the volume of the box by multiplying its length, width, and height.
Assuming the box is a rectangular prism and the dimensions are not given in the question, we cannot determine the exact volume of the box. Therefore, let's represent the volume of the box as V.
The percentage of the box's volume occupied by the cards can be calculated as follows:
Percentage of the box's volume = (Volume of the stack / Volume of the box) * 100
Percentage of the box's volume = ((32 inches) / V) * 100
However, since the exact volume of the box is not given, we cannot calculate the exact percentage of the box's volume occupied by the cards.
To determine the exact percentage, we would need additional information, such as the dimensions of the box or the volume it can hold. Without that information, we can only say that the percentage of the box's volume occupied by the cards is undetermined.