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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

x + 4/7

step-by-step explanation:

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