Answer:
The volume of the observatory is 497.43 [tex]feet^{3}[/tex]
Step-by-step explanation:
i) The diameter of the floor is 10 feet. The floor is circular and has a radius,
r = [tex]\frac{10}{2}[/tex] = 5 feet.
Therefore the area of the circular floor of the observatory
= [tex]\pi r^{2}[/tex] = 3.14159 × [tex]5^{2}[/tex] = 78.54 [tex]feet^{2}[/tex]
ii) The observatory is made up of two parts
a) 3 foot tall cylinder
∴ volume of cylinder = [tex]\pi r^{2}[/tex] × h
= 78.54 × 3
= 235.62 [tex]feet^{3}[/tex]
b) hemisphere = [tex]\frac{1}{2}[/tex] × [tex]\frac{4}{3} \pi r^{3}[/tex] = 0.6667 × 78.54 × 5 = 261.81 [tex]feet^{3}[/tex]
c) Therefore the total volume of the observatory is = a) + b)
= 235.62 + 261.81 = 497.43 [tex]feet^{3}[/tex]
