Task of the Week: Water in the Fountain

Fountains and their volume are ideal for modeling different geometric bodies. While many of the fountains have a rectangular or circular shape and can thus be approximated as cuboid or cylinder, in the current “Task of the Week” we present an octagonal fountain whose volume can be described by a prism with an octagonal area.

Task: Water in the Fountain (Task Number: 4295)

What is the approximate volume of water in this fountain? Assume that the average depth of the water is about 30 cm. Give the result in liters.

Even if the formula for an octagon is not known, the task can be solved by dividing the area or completing the area. For example, one can determine the area of the square enclosing the octagon. Then, for each corner which is calculated too much in the square, the area of a triangle must be substracted. The height is then used to calculate the volume.