__Category__: Solid Geometry, Plane Geometry"Published in Newark, California, USA"

A vessel is in the form of an inverted regular square pyramid of altitude 9.87 in. and a base edge 6.27 in. The depth of the water it contains is 6 in. How much will the surface rise when 1 pint of water is added? (One gallon = 231 cubic inches) Find the wetted surface when the depth of the water is 9.23 in.

__Solution__:

To illustrate the problem, let's draw the figure and label as follows

Photo by Math Principles in Everyday Life |

The volume of the empty vessel is calculated as follows

When the depth of the water is 6 in, the volume is calculated by ratio and proportion as follows

Therefore, after the addition of 1 pint of water, the height of water can be calculated by ratio and proportion as follows

The difference of the height of water after the addition of 1 pint of water is

When the depth of the water is 9.23 in, the length of a square base is calculated by ratio and proportion as follows

By Pythagorean Theorem, the slant height will be equal to

Photo by Math Principles in Everyday Life |

Therefore, the wetted surface of a vessel is