To find the volume of unused space in the box, we first need to calculate the volume of the box itself and then the total volume of the soda cans that fit inside it.
The dimensions of the box are 4.8 inches (width) × 21 inches (length) × 7 inches (height). So, we can calculate the volume of the box using the formula for the volume of a rectangular prism:
Volume of the box = width × length × height
Volume of the box = 4.8 in × 21 in × 7 in = 705.6 cubic inches.
Next, let’s calculate the volume of one soda can. The formula for the volume of a cylinder (which a soda can resembles) is:
Volume of the can = π × (radius²) × height
Given the diameter of the soda can is 3.5 inches, the radius will be half of that:
Radius = 3.5 in ÷ 2 = 1.75 in
Now, substituting the values into the volume formula:
Volume of one can = π × (1.75 in)² × 4.8 in ≈ 3.14 × 3.0625 in² × 4.8 in ≈ 46.2 cubic inches.
Since the box holds 12 cans:
Volume of 12 cans = 12 × 46.2 cubic inches ≈ 554.4 cubic inches.
Finally, to find the unused volume in the box, we subtract the total volume of the cans from the volume of the box:
Unused volume = Volume of the box – Volume of 12 cans
Unused volume = 705.6 cubic inches – 554.4 cubic inches = 151.2 cubic inches.
Therefore, the volume of the box that is going unused is approximately 151.2 cubic inches.