Let G be the solid in the first octant that is bounded by the cone z = V3r? + 3y2 and the planes z = 3, x = 0 and y = 0. (a) Find the volume of G using cylindrical coordinates.

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Let G be the solid in the first octant that is bounded by the cone z =
3x2 +3y2 and the
planes z =
3, * =
O 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 + z?.
Transcribed Image Text:Let G be the solid in the first octant that is bounded by the cone z = 3x2 +3y2 and the planes z = 3, * = O 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 + z?.
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