These ice-block trays mould ice into blocks called “hex cubes”. Are they cubes? What is their geometric name?
There are two sizes of blocks that can be made. Estimate the ratio of the volume of a large ‘hex cube’ to the volume of a small ‘hex cube’.
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Ice-Block Trays
Answer:
A cube has 6 square faces, so the ice-block trays are not making cubes. They are making prisms with a base that is a regular hexagon. Prisms are named after the shape of their bases, so they are regular hexagonal prisms. Because they have 8 faces, they could also be called octahedrons.
From the photograph, it looks like a large ‘hex cube’ has edges that are twice the length of the edges of the small hex cube.
Because these two objects are similar (meaning that they have the same shape):
- the area of each face on the large hex cube is 2 x 2 = 4 times the area of each face of the small hex cube.
- the volume of the large hex cube is 2 x 2 x 2 = 8 times the volume of the small hex cube.
Therefore the ratio of the volume of the large hex cube to the volume of the small hex cube is estimated to be 8:1.