Question

How much glass is needed to construct a hexagonal (6-sided) fish tank? The tank is

4 feet tall and each pane is 11 feet wide. The tank's bottom is not made of glass.

Answer 1

To construct a hexagonal fish tank, we can calculate the total area of the six panes of glass by finding the width and height of each pane using trigonometric functions and geometry formulas. We can then multiply the area of each pane by the number of panes to determine the total amount of glass needed.

Step-by-step explanation:

To determine how much glass is needed to construct a hexagonal fish tank, we need to calculate the total area of the six panes of glass that make up the tank. Since the tank is 4 feet tall, each pane is 4 feet in height as well. To find the width of each pane, we need to first calculate the apothem, which is the distance from the center of the hexagon to the midpoint of any side. The formula to find the apothem is: apothem = (side length) / (2 * tan(angle)). With the side length of the hexagon being 11 feet, and the angle of each corner being 120 degrees, we can calculate the apothem as follows: apothem = 11 / (2 * tan(120)). Once we have the apothem, we can find the width of each pane by doubling the apothem and adding the side length of the hexagon: width = (2 * apothem) + side length. With the width of each pane determined, we can calculate the area of each pane as: area = width * height. Finally, we can find the total amount of glass needed by multiplying the area of each pane by the number of panes, which is 6 in this case.

Answer 2

Each side of the hexagon is a rectangle of height 4ft and width 11ft.

The area of each one of these rectangles is:

A = 4ft*11ft = 44ft^2

And a hexagon has 6 faces, so the fish tank will have 6 of these rectangles, then the total area is:

area = 6*44ft^2 = 264 ft^2

We know that the base of the hexagon is not made of glass, but we do not know if the top is made of glass or not.

In the case that the top is not made of glass, the amount of glass needed is 264 ft^2

If the top is made of glass, then we need to add the area of a hexagon of side 11 ft, which is:

a = (3*√3)*(11ft)^2/2 = 314.4ft^2

Then the total area in this case is:

264 ft^2 + 314.4ft^2 = 578.4 ft^2

This is the total amount of glass needed to construct the tank if the top of the tank is made of glass.