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Putnam
2006 Putnam
A1
Putnam 2006 A1
Putnam 2006 A1
Source:
December 4, 2006
Putnam
analytic geometry
calculus
integration
trigonometry
geometry
projective geometry
Problem Statement
Find the volume of the region of points
(
x
,
y
,
z
)
(x,y,z)
(
x
,
y
,
z
)
such that
(
x
2
+
y
2
+
z
2
+
8
)
2
≤
36
(
x
2
+
y
2
)
.
\left(x^{2}+y^{2}+z^{2}+8\right)^{2}\le 36\left(x^{2}+y^{2}\right).
(
x
2
+
y
2
+
z
2
+
8
)
2
≤
36
(
x
2
+
y
2
)
.
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