Use spherical coordinates to find the volume of the solid E that
lies below the cone...
Use spherical coordinates to find the volume of the solid E that
lies below the cone z = sqrt x^2 + y^2, and within the sphere x^2 +
y^2 + z^2 = 2, in the first octant.
Use spherical coordinates to find the volume of solid within the
sphere x^2 + y^2 + z^2 = 16 and above the cone 3z^2 = x^2 + y^2 and
lying in the 1st octant.
Find the volume of the solid using triple integrals. The solid
bounded below by the cone
z= sqr
x2+y2 and bounded above by the sphere
x2+y2+z2=8.(Figure)
Find and sketch the region of integration R.
Setup the triple integral in Cartesian coordinates.
Setup the triple integral in Spherical coordinates.
Setup the triple integral in Cylindrical coordinates.
Evaluate the triple integral in Cylindrical coordinates.
Use cylindrical or spherical coordinates, whichever seems more
appropriate. Find the volume of the smaller wedge cut from a sphere
of radius 2 by two planes that intersect along a diameter at an
angle of ?/2.
Set up a triple integral for the volume of the solid that lies
below the plane x + 2y + 4z = 8, above the xy-plane, and in the
first octant.
Hint: Try graphing the region and then projecting into the
xy-plane. To do this you need to know where the plane
x+ 2y + 4z = 8 intersects the xy-plane (i.e. where z = 0).
Use spherical coordinates.Find the centroid of the solid E that
is bounded by the xz-plane and the hemispheres y = 16 − x2 − z2 and
y = 64 − x2 − z2 . (x, y, z) =