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Unformatted text preview: solid wooden ball (sphere) of radius R and drilling a
hole of radius a straight through the center. (The hole is cylindrical in shape with radius a, and the
resulting solid has ﬂat edges at its top and bottom.) Find the volume of the napkin ring, in terms of
R and a.
o / o a
R
/ Math 42, Winter 2010 First Exam — January 28, 2010 Page 11 of 11 8. (8 points) A fuel tank buried underground has the shape of a circular cylinder lying lengthwise (so
that the axis of symmetry is horizontal, i.e., parallel to the ground). The radius of the cylinder is 6
feet, the length is 30 feet, and the top of the tank is 4 feet below ground level.
Suppose that the tank is completely ﬁlled with a liquid that has weight density 40 lb/ft3 . Set up an
integral in terms of a single variable that represents the amount of work it takes to pump half of the
liquid out of the tank and up to ground level. Show all your steps in setting up the integral, but do
not evaluate it....
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This note was uploaded on 07/31/2013 for the course MATH 42 taught by Professor Butscher,a during the Spring '07 term at Stanford.
 Spring '07
 Butscher,A
 Math, Calculus

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