3. Let G be the solid in the first octant that is bounded by the cone z = V3x2 + 3y2 and the planes z = 3, x = 0 and y = 0. (a) Find the volume of G using cylindrical coordinates. (b) Use spherical coordinates to set-up a triple integral equal to the mass of G given the density function 8(x, y, z) = x² + y² + z².

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3. Let G be the solid in the first octant that is bounded by the cone z =
V3.x2 + 3y? and the
planes z = 3, x = 0 and y = 0.
(a) Find the volume of G using cylindrical coordinates.
(b) Use spherical coordinates to set-up a triple integral equal to the
mass of G given the density function 8(x, y, z) = x² + y² + z².
Transcribed Image Text:3. Let G be the solid in the first octant that is bounded by the cone z = V3.x2 + 3y? and the planes z = 3, x = 0 and y = 0. (a) Find the volume of G using cylindrical coordinates. (b) Use spherical coordinates to set-up a triple integral equal to the mass of G given the density function 8(x, y, z) = x² + y² + z².
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