Honors Calculus I
Quiz 14
1.
Determine the centroid of the area bounded by the
x–
axis,
f
(
x
)
=
x
n
, and the
vertical line
x
=
1
.
2.
Determine the centroid of the area within a circle in the first quadrant.
3.
Use Pappus’ Theorem to determine the volume of a torus.
The torus is the area of
a circle of radius
a
rotated about the
y
–axis.
The center of the circle is distance
b
from the
y
–axis.
4.
Use Pappus’ Theorem to determine the surface area of the torus in the previous
problem.
5.
Determine the surface area of a right circular cone having radius
a
and height
h
.
6.
Consider a square with sides length
a
and with center distance
b
away from the
y
–
axis.
What is the volume obtained by rotating this figure about the
y
–axis?
7.
What is the surface area of the figure described in the previous problem?
8.
What is the length of the parabola given by the graph of
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 Spring '07
 JURY
 Calculus, Cone

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