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Two Glasses

by Serhiy Grabarchuk Jr

Solution Step 0/0

One glass is a perfect parallelepiped with a square base and another – a perfect cylinder. Each can contain 600ml of water when brimful.

If 600ml is the largest volume of water a glass can hold when brimful, what is the next largest volume which can be precisely obtained using only these two glasses as measuring tools?

Explanations

Fill out the parallelepiped glass till the rims. The cylinder glass is empty. Now tilt the brimful parallelepiped glass in such a way that the water pours out of it into the cylinder glass until the water level passes through three corners of the parallelepiped glass – one top corner and two bottom corners – as shown in shape A. The volume of the water left in the parallelepiped glass equals a triangular prism. The volume of the prism equals 1/6 of the glass or 100ml. This means the volume of the water poured into the cylinder glass equals 600ml – 100ml = 500ml.

The shape B illustrates how in the same way of tilting the 300ml can be obtained in the parallelepiped glass when the water level passes through 4 corners – a pair of bottom and a pair of top ones.

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