A restaurant has a giant fish tank, shown at the right in the shape of an octagonal prism. Find the volume and surface area of the fish tank if the base is a regular octagon with the side length 0.6m and the height of the prism is 3m.

Step-by-step explanation:

The octagonal prism is made up of 8 rectangular sides and 2 octagonal bases. We would determine the surface area by applying the formula,

Surface area = 2 * area of octagonal base + (number of sides * area of rectangular face)

Area of rectangular face = 0.6 * 3 = 1.8m²

To determine the area of the base, we would determine the length of the apotherm, a by applying the formula,

a = s/2tan (180/n)

n = number of sides = 8

s = length of each side

a = 0.6/2tan (180/8) = 0.6/2tan22.5

a = 0.72

Also,

a = 2A/p

Where

A = area of octagonal base

p = perimeter of octagonal base

p = number of sides * side length

p = 8 * 0.6 = 4.8m

Therefore,

0.72 = 2A/4.8

A = (0.72 * 4.8) / 2 = 1.728m²

Therefore,

Surface area = (2 * 1.728) + (8 * 1.8)

Surface area = 17.856m²

The formula for determining the volume is

Volume = base area * height

Volume = 1.728 * 3 = 5.184m³