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Solve the Problem VtV _ { t } Be the Volume of the Tetrahedron Bounded by the Coordinate

Question 226

Multiple Choice

Solve the problem.
-Let VtV _ { t } be the volume of the tetrahedron bounded by the coordinate planes and the plane x3+y4+z3=1\frac { x } { 3 } + \frac { y } { 4 } + \frac { z } { 3 } = 1 , and let VeV _ { e } be the volume of the ellipsoid x29+y216+z29=1\frac { x ^ { 2 } } { 9 } + \frac { y ^ { 2 } } { 16 } + \frac { z ^ { 2 } } { 9 } = 1 . Find the quotient VeVt\frac { V _ { e } } { V _ { t } } .


A) 4π3\frac { 4 \pi } { 3 }
B) 4π4 \pi
C) 2π3\frac { 2 \pi } { 3 }
D) 8π8 \pi

Correct Answer:

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