Question

A hemispherical dome of radius 40 feet is to be given 7 coats of paint, each of which is 1/100 inch thick. How do you use linear approximation to estimate the volume of paint needed for the job?

Answer 1

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Answer 2

V=(1/2)(4pi r^3/3)=2pi r^3/3.

first,we find the equation of the tangent line to V at r=40 ft.

point:(40,128000 pi/3)

slope: V' =2 pi r^2;at r=40 we get 3200 pi.

So,V=(approx.)128000 pi/3+3200 pi (r -40).

since 5/100 in =1/20 in= 1/240 ft {via 1 ft =12 in }, we want

V{(40+1/240)ft}=(approx.)128000 pi/3+3200 pi (1/240).

=128040 pi /3 cubic feet.

I Hope this Helps......