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A solid has the shape of a sphere of radius a. Find the mass of the solid if the density at a point P is equal to the distance from the center to P.

Answer: $\pi a^4$

A homogeneous solid is bounded by the graph of z=9-x²-y², the interior of the cylinder x²+y²=4, and the xy-place. Find the mass and the center of mass.

Answer: $28\pi$ ; (0,0,151/42)

Find the volume and centroid of the solid bounded by the graphs of z=x², z=4, y=0, and y+z=4.

Answer: 256/15; (0, 8/7, 12/7)

Find the mass of the solid that lies outside the sphere x²+y²+z²=1 and inside the sphere x²+y²+z²=4 if the density at a point P is equal to the square of the distance from the center of the spheres to P.

Answer: $124\pi/5$

A homogeneous solid is bounded by the graphs of $z=\sqrt{x^{2}+y^{2}}$ and z=x²+y². Find the center of mass.

Answer: $\pi/6$ ; (0,0,1/2)

The density at a point P of a spherical solid of radius a is equal to the distance from P to a vertical line through the center of the solid. Find the mass of the solid.

Answer: $\pi^{2}a^{4}/4$

The density at a point P in a cubical solid of edge a is equal to the square of the distance from P to a fixed corner of the cube. Find the center of mass.

Answer: (7a/12, 7a/12, 7a/12)

Let Q be the tetrahedron bounded by the coordinate places and the plane 2x+5y+z=10. Find the center of mass if the density at the point P=(x,y,z) is equal to the distance from the xz-plane to P.

Answer: 25/3; (1, 4/5, 2)

Find the volume of the solid that lies above the cone z²=x²+y² and inside the sphere x²+y²+z²=4z.

Answer: $8\pi$

About this document ...

This document was generated using the LaTeX2HTML translator Version 97.1 (release) (July 13th, 1997)

The command line arguments were:
latex2html -link 0 -split 0 -t Triple Integral Word Problems triplewords.tex.

The translation was initiated by Joshua Holden on 11/10/1999

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Joshua Holden
11/10/1999