### Brain Teasers

# Water and Ice

When water changes into ice, the volume increases by one ninth. Consider a 20 cm-tall cylindrical beaker, full of ice. On top of the beaker, there is a cone of ice of the same diameter and 5 cm-tall. When all the ice melts into water, what is the height of the water in the beaker?

### Hint

Is the cylinder enough to hold all the water?### Answer

When water changes into ice, the volume increases by one ninth. This means that the ratio of the volumes of water and ice is 9:10.A 5 cm-tall cone of ice is as large as a 5/3 cm-tall cylinder, which makes a total of 20+5/3=65/3 cm of ice, and will yield 65/3*9/10=19.5 cm of water. Because 19.5<20, the cylinder itself can hold all the water, and the cone is emptied. Therefore, the height of water is 19.5 cm.

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