Answer:
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