Question

4 jenn noticed that she can fit two juice boxes side by side on the bottom of this box. she can make two more layers like the one shown to fill the box. using a juice box as a measure of volume, what is the volume of the larger box?
solution
5 a box is 2 inches long, 1 inch wide, and 6 inches tall. what is the relation between the volume of this box and the one in problem 4? tell how you...

Explanation:

Problem 4

Step1: Determine number of juice boxes per layer

Jenn can fit 2 juice boxes per layer (side by side on the bottom).

Step2: Determine number of layers

She can make 2 more layers like the shown one, so total layers = 1 (shown) + 2 = 3 layers.

Step3: Calculate total number of juice boxes

Total juice boxes = number of juice boxes per layer × number of layers = \( 2 \times 3 = 6 \). Since each juice box is a unit of volume, the volume of the larger box is the number of juice boxes.

Step1: Calculate volume of the box

Using the formula \( V = l \times w \times h \), substitute the values: \( V = 2 \times 1 \times 6 = 12 \) cubic inches.

Step2: Compare with Problem 4 (assuming Problem 4's volume in cubic inches or relevant unit, but since Problem 4 was in juice box units, we need to know the volume of one juice box. However, if we assume the juice box in Problem 4 has volume equal to this box or we compare the numbers: The volume here is 12, and Problem 4 was 6 (if juice box volume is 2 cubic inches, but likely the relation is that this box's volume is twice (or some multiple) of Problem 4's. But since the question is about the relationship, we state the volume of this box is \( 2 \times 1 \times 6 = 12 \) and compare to Problem 4's 6 (if juice box is 2 each, then 6 juice boxes would be 12, so equal. Or if juice box volume is different, but based on calculation, this box's volume is 12.

Answer:

6 (juice box units)

Problem 5

First, calculate the volume of this box. The volume of a rectangular box is given by \( V = l \times w \times h \), where \( l = 2 \) inches, \( w = 1 \) inch, \( h = 6 \) inches.