ANSWER
636,255 cubic centimeters
EXPLANATION
Given:
Thickness = 0.02 cm
Diameter = 45m = 4500cm
Recall, Volume of a sphere is:
[tex]V=\frac{4}{3}\pi r^3[/tex]
Determine change in V by differentiating the Volume:
[tex]\begin{gathered} \Delta V=dV=3\times\frac{4}{3}\pi r^{3-1}dr \\ dV=4\pi r^2dr \end{gathered}[/tex]
Note: from the given question
dr = 0.02cm
r = 4500/2 = 2250 cm
Recall: for Hemisphere
[tex]\begin{gathered} dV=\frac{1}{2}\times4\pi r^2dr \\ dV=2\pi r^2dr \end{gathered}[/tex]
Substitute the values:
[tex]\begin{gathered} dV=2\times3.142\times(2250)^2\times0.02 \\ dV=6.284\times5062500\times0.02 \\ dV=636255cm^3 \end{gathered}[/tex]
Hence, the amount of paint needed is 636,255 cubic centimeters.
