Question 1205513
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"Use tables"...?<br>
The ratio of the volume of water to the volume of the vessel is 1:2.  By a powerful general principle regarding similar figures, the ratio of corresponding linear measurements in the two figures is {{{1:root(3,2)}}}.<br>
The depth of the vessel is 10cm; the depth of the water in cm is<br>
{{{10/root(3,2)}}} = 7.937 to 3 decimal places<br>
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Further notes....<br>
In case you are not familiar with the basic principle here....<br>
If the scale factor (ratio of linear measurements) between two similar figures is A:B, then the ratio of corresponding area measurements is A^2:B^2, and the ratio of corresponding volume measurements is A^3:B^3.<br>
In this problem, given 1:2 as the ratio of volumes, the ratio of depths (a linear measurement) is {{{1:root(3,2)}}}<br>