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1 February, 05:25

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.

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  1. 1 February, 08:00
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    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
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