Painting a dome - Math Central

HOME

Math Central

Quandaries & Queries

Question from Jessica, a student:

A hemispherical dome with a radius of 50 ft will be given a coat of paint .01 inch thick.
The Contractor for the job wants to estimate the number of gallons of paint needed.
Use a differential to obtain an estimate (231 cubic inches/gallon) HINT: Approximate the change
in volume of hemisphere corresponding to increase of .01 inch in the radius.

The answer is 98 gallons but I simply cannot get that answer
Any help would be appreciated

I do (at least approximately, I did not actually use a calculator)

Are you starting with the volume of a hemisphere?
Are you ignoring the flat horizontal surface?
Are you converting the radius to 600 inches?

My approximation was

2 × π × r² × dr ~ 22000 cubic inches ~ 100 gallons.

Good Hunting!
RD

Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.