Let's say a company is manufacturing juice boxes that are rectangular prisms with dimensions 4 inches by 3 inches by 4 inches. The company has a warehouse whose dimensions are 40 feet by 30 feet by 20 feet. If the company makes 200,000 juice boxes, will it be able to store all of the juice boxes in the warehouse?
(40*12*30*12*20*12)/(200000*(4*3*4)) = 4.32
so, yes, the warehouse is plenty big enough.
Or, considering that 1 ft^3 holds 36 boxes, it requires only 5555.5 ft^3 for the whole batch, and the room is 24,000 ft^3, there's plenty of room.
To determine if the company will be able to store all the juice boxes in the warehouse, we first need to calculate the volume of the juice boxes and the volume of the warehouse.
The volume of a rectangular prism can be calculated using the formula: volume = length * width * height.
The volume of one juice box with dimensions 4 inches by 3 inches by 4 inches is:
Volume of one juice box = 4 inches * 3 inches * 4 inches = 48 cubic inches.
Now, we need to convert the dimensions of the warehouse from feet to inches since the dimensions of the juice boxes are given in inches.
40 feet = 40 * 12 = 480 inches.
30 feet = 30 * 12 = 360 inches.
20 feet = 20 * 12 = 240 inches.
The volume of the warehouse is:
Volume of warehouse = 480 inches * 360 inches * 240 inches.
To determine if all the juice boxes can fit inside the warehouse, we divide the volume of the warehouse by the volume of one juice box.
Number of juice boxes that can be stored = Volume of warehouse / Volume of one juice box.
Now, let's plug the numbers into the equation:
Number of juice boxes that can be stored = (480 inches * 360 inches * 240 inches) / 48 cubic inches.
After calculating this equation, we find that the number of juice boxes that can be stored in the warehouse is:
Number of juice boxes = 5,760,000.
Since the company is manufacturing only 200,000 juice boxes, which is significantly less than the capacity of the warehouse, the answer is yes, the warehouse will be able to store all of the juice boxes.