Question

Please help me work through this thank you! read the question carefully since it can be confusing

Answer 1

636,255 cubic centimeters

Step-by-step explanation

Given:

Thickness = 0.02 cm

Diameter = 45m = 4500cm

Recall, Volume of a sphere is:

`V=(4)/(3)\pi r^3`

Determine change in V by differentiating the Volume:

`\begin{gathered} \Delta V=dV=3*(4)/(3)\pi r^(3-1)dr \\ dV=4\pi r^2dr \end{gathered}`

Note: from the given question

dr = 0.02cm

r = 4500/2 = 2250 cm

Recall: for Hemisphere

`\begin{gathered} dV=(1)/(2)*4\pi r^2dr \\ dV=2\pi r^2dr \end{gathered}`

Substitute the values:

`\begin{gathered} dV=2*3.142*(2250)^2*0.02 \\ dV=6.284*5062500*0.02 \\ dV=636255cm^3 \end{gathered}`

Hence, the amount of paint needed is 636,255 cubic centimeters.