These exercises reference the Theorem of Pappus : If R is a bounded plane region and L is a line that lies in the plane of R such that R is entirely on one side of L , then the volume of the solid formed by revolving R about L is given by volume = area of R ⋅ distance traveled by the centroid Use the Theorem of Pappus and the result of Example 3 to find the volume of the solid generated when the region bounded by the x -axis and the semicircle y = a 2 − x 2 is revolved about (a) the line y = − a (b) the line y = x − a .
These exercises reference the Theorem of Pappus : If R is a bounded plane region and L is a line that lies in the plane of R such that R is entirely on one side of L , then the volume of the solid formed by revolving R about L is given by volume = area of R ⋅ distance traveled by the centroid Use the Theorem of Pappus and the result of Example 3 to find the volume of the solid generated when the region bounded by the x -axis and the semicircle y = a 2 − x 2 is revolved about (a) the line y = − a (b) the line y = x − a .
These exercises reference the Theorem of Pappus: If R is a bounded plane region and L is a line that lies in the plane of R such that R is entirely on one side of L, then the volume of the solid formed by revolving R about L is given by
volume
=
area of
R
⋅
distance
traveled
by
the
centroid
Use the Theorem of Pappus and the result of Example 3 to find the volume of the solid generated when the region bounded by the x-axis and the semicircle
y
=
a
2
−
x
2
is revolved about
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