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Answer:
The volume of the observatory is 497.43
Step-by-step explanation:
i) The diameter of the floor is 10 feet. The floor is circular and has a radius,
r = = 5 feet.
Therefore the area of the circular floor of the observatory
= = 3.14159 ×
= 78.54
ii) The observatory is made up of two parts
a) 3 foot tall cylinder
∴ volume of cylinder = × h
= 78.54 × 3
= 235.62
b) hemisphere = ×
= 0.6667 × 78.54 × 5 = 261.81
c) Therefore the total volume of the observatory is = a) + b)
= 235.62 + 261.81 = 497.43
Knowing that cos(45°) = 1/√2 is the way forward.
The last step in the equation may not be obious, but the trick here is to multiple numerator and denominator with (1-√2), then the denominator has the special product (a+b)(a-b) = a²-b².
The last step in the equation may not be obious, but the trick here is to multiple numerator and denominator with (1-√2), then the denominator has the special product (a+b)(a-b) = a²-b².