Cathedral roof sphere

Cathedral height is 110 m, sphere weight 6000 kg, dome diameter 43 m, crane arm length 25 m
a) what was the diameter of this sphere?
b) how much mechanical work had to be done to lift it to the designated place?

Final Answer:

D =  43 m
W =  3300000 J

Step-by-step explanation:

$$\begin{gathered} h=110\text{m} \\ m=6000\text{kg} \\ D=43\text{m} \\ r=25\text{m} \\ D=43=43\text{m} \end{gathered}$$

$$\begin{gathered} g=10{\text{m/s}}^2 \\ {m}_2=m/2=6000/2=3000\text{kg} \\ W=m_2\cdot g\cdot h=3000\cdot 10\cdot 110=3300000\text{J} \end{gathered}$$

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