Question

Find the volume of the solid region which lies inside the sphere x^2 + y^2 + z^2 = 4z and outside of the cone z^2 = x^2 + y^2.

Answer #1

Find the volume of the solid that lies under the paraboloid z =
x^2 + y^2 , above the xy-plane and inside the cylinder x^2 + y^2 =
1.

The domain E of R^3 located inside the sphere x^2 + y^2 + z^2 =
12 and above half-cone z = sqrroot(( x^2 + y^2) / 3) (a) Represent
the domain E.
(b) Calculate the volume of solid E with a triple integral in
Cartesian coordinates.
(c) Recalculate the volume of solid E using the cylindrical
coordinates.

In spherical coordinates, find the volume of the region bounded
by the
sphere x^2 + y^2 + z^2 = 9 and the plane z = 2.

Find the position of the center of mass of the solid defined by
the region inside the sphere x^2 + y^2 + z^2 = 2
and above the paraboloid z = x^2 + y^2 .
The density is ρ (x, y, z) = z [kg / m3 ].

3. Find the volume of the solid obtained by revolving the region
below y = 4 − x 2 and above y = 0, for 0 ≤ x ≤ 2, about the
y-axis.
4. Find the centroid of the region outside the circle x 2 + (y +
4)2 = 25 and inside the circle x 2 + y 2 = 9.

find the volume between the cone z=sqrt(x^2+y^2) and the sphere
x^2+y^2+z^2=2az, if a=1

Find the integral that represents:
The volume of the solid under the cone z = sqrt(x^2 + y^2) and
over the ring 4 ≤ x^2 + y^2 ≤ 25
The volume of the solid under the plane 6x + 4y + z = 12 and
on the disk with boundary x2 + y2 = y.
The area of the smallest region, enclosed by the spiral rθ =
1, the circles r = 1 and r = 3 & the polar...

4. Let W be the three dimensional solid inside the sphere x^2 +
y^2 + z^2 = 1 and bounded by the planes x = y, z = 0 and x = 0 in
the first octant. Express ∫∫∫ W z dV in spherical coordinates.

Find the volume of the solid obtained by rotating the region
bounded by x = y^2 and x = |y| about the y-axis.?

Use polar coordinates to find the volume of the given solid.
Inside the sphere x2 + y2 + z2
= 16 and outside the cylinder x2 + y2 = 4

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