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Calculus II Quiz
#5 March
17, 2003

Name____________________ R. Hammack Score
______

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(1) Consider the region contained between
the graphs of , ,
and .
This region is revolved around the x-axis.
Find the volume of the resulting solid.

The cross section at x is a circle of radius so
the cross sectional area is .

Using the slicing formula, the volume is

cubic units.

(2)
Consider the region contained between the graphs of , , y=1, and
.
This region is revolved around the x-axis.
Find the volume of the resulting solid.

Using the formula for volumes by shells,

cubic
units