Use linear approximation to estimate the amount of paint

Question

Use linear approximation to estimate the amount of paint in cubic centimetres needed to apply a coat of paint 0.010000cm thick to a hemispherical dome with a diameter of 60.000 meters. 

Answer 1

REMEMBER- given information is in two different units and the answer must be in cubic cm

 

Volume of a sphere = 4/3 π r^3

 

Therefore, for a hemisphere, V= 2/3 pi r^3

                                          dV = 2pir^2 dr where dr=0.01cm and r=(1/2)*60m=3000cm

 

Now we have, dV = 2*pi*(3000^2)*(.01) = 565,486.68 cubic centimeters