Question

Let D be the smaller cap cut from a solid ball of radius 2 units by a plane 1 unit from the center of the sphere. Express the volume of D as an interated triple integral in (a) spherical and (b) cylindrical coordinates. I was able to calculate the rectangular coordinates, however I do not understand how I should converse those to spherical and cylindrical coordinates.

Answer #1

a
ball p = 2 is cut by the z plane = 1. If D is a smaller piece of
ball, sketch D! without calculating, determine the triple integral
and its boundaries to calculate volume D using:
a. Cartesian coordinates
b. cylinder coordinates
c. spherical coordinates

Find the volume of the solid using triple integrals. The solid
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Find and sketch the solid and the region of integration R. Setup
the triple integral in Cartesian coordinates. Setup the triple
integral in Spherical coordinates. Setup the triple integral in
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Let E be the solid that lies in the first octant, inside the
sphere x2 + y2 + z2 = 10. Express the volume of E as a triple
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Set up (Do Not Evaluate) a triple integral that yields the
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the sphere x^2+y^2+z^2=8
and above the cone z^2=1/3(x^2+y^2)
a) Rectangular coordinates
b) Cylindrical
coordinates
c) Spherical
coordinates

Lets consider the solid bounded above a sphere x^2+y^2+z^2=2 and
below by the paraboloid z=x^2+y^2.
Express the volume of the solid as a triple integral in
cylindrical coordinates. (Please show all work clearly) Then
evaluate the triple integral.

A sphere with a radius of 3 units is cut with a plane at a
distance of 2 units from its center. Small cut Calculate the volume
of the part.

1- Set up the triple integral for the volume of the sphere Q=8
in rectangular coordinates.
2- Find the volume of the indicated region.
the solid cut from the first octant by the surface z= 64 - x^2
-y
3- Write an iterated triple integral in the order dz dy dx for
the volume of the region in the first octant enclosed by the
cylinder x^2+y^2=16 and the plane z=10

A solid insulating sphere of radius a = 2 cm carries a net
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value of 77.1 N/C.
what is the surface charge density on the surface of the inner
ball?...

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