A hemispherical dome with radius 50 feet will be given a
coat of paint 0.01 inch thick. The contractor for the job
wants to estimate the number of gallons of paint that will
be needed. Use differentials to obtain an estimate (there
are 231 cubic inches in a gallon). HINT:Approximate the
change in the volume of the hemisphere corresponding to
an increase of 0.01 inch in the radius.

Question

A hemispherical dome with radius 50 feet will be given a
coat of paint 0.01 inch thick. The contractor for the job
wants to estimate the number of gallons of paint that will
be needed. Use differentials to obtain an estimate (there
are 231 cubic inches in a gallon). HINT:Approximate the
change in the volume of the hemisphere corresponding to
an increase of 0.01 inch in the radius.

anonymous · Answer

volume of a 1/2 sphere = (2/3)pi r^3

dV = 2pi r^2 dr

r = 50ft = 600in
dr=0.01in

dV = 2 pi (600^2)(0.01)

= (some value) cubic inches (i dont have a calculator)

no. of gallons = (some value)/(231 cubic in per gallon)

anonymous · Answer

yep i ending up getting 98 gallons