Question

Please help me I really need help i beg of u due today

Answer 1

Answer:

The volume of the observatory is 497.43 $feet^{3}$

Step-by-step explanation:

i) The diameter of the floor is 10 feet. The floor is circular and has a radius,          

    r =  $\frac{10}{2}$ = 5 feet.

   Therefore the area of the circular floor of the observatory

     = $\pi r^{2}$      =   3.14159 × $5^{2}$    =    78.54 $feet^{2}$

ii) The observatory is made up of two parts

  a)  3 foot tall cylinder

      ∴ volume of cylinder = $\pi r^{2}$   × h

                                         = 78.54 × 3

                                         = 235.62 $feet^{3}$

   b)  hemisphere = $\frac{1}{2}$ × $\frac{4}{3} \pi r^{3}$ = 0.6667 × 78.54 × 5   =  261.81 $feet^{3}$

    c) Therefore the total volume of the observatory is = a) + b)

         = 235.62 + 261.81 =   497.43 $feet^{3}$