A farmer makes hay bales that are 1m cubes. His trailer can haul 128 hay bales at once. He is going to buy a new machine that makes hay bales that are 2cm cubes. How many bales will fit on the trailer now? (Assume they all fit evenly)

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Do you mean that the new machine's bales are 2 cm cubes?

a 2m cube occupies 8 times the volume of a 1m cube. I assume the trailer is enclosed, so the volume makes a difference. So, what's 128/8?

To find out how many bales of hay that can fit on the trailer now, we need to compare the volume of the two types of hay bales.

First, let's calculate the volume of the old hay bale, which is a cube with a side length of 1 meter:

Volume = (side length)^3 = (1m)^3 = 1 cubic meter

Next, let's calculate the volume of the new hay bale, which is a cube with a side length of 2 centimeters. Since the side length is in centimeters, let's convert it to meters:

1 centimeter = 0.01 meters

Therefore, the side length of the new hay bale in meters is:

2 centimeters * 0.01 = 0.02 meters

Now, calculate the volume:

Volume = (side length)^3 = (0.02m)^3 = 0.000008 cubic meters

Now we can compare the volumes:

Old hay bale volume: 1 cubic meter
New hay bale volume: 0.000008 cubic meters

To find the number of new hay bales that can fit in the trailer, divide the trailer's capacity by the volume of each new hay bale:

Number of new hay bales = Trailer capacity / New hay bale volume

Trailer capacity = 128 hay bales

Number of new hay bales = 128 / 0.000008

Simplifying the division, we have:

Number of new hay bales = 16,000,000

Therefore, the new machine can make 16,000,000 hay bales that are 2cm cubes, which can fit on the trailer.