Question

Use cylindrical coordinates.

Find the volume of the solid that is enclosed by the cone

z =

x^{2} + y^{2} |

and the sphere

x^{2} + y^{2} + z^{2} = 128.

Answer #1

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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

Use cylindrical coordinates to find the volume of the solid
bounded by the graphs of z = 68 − x^2 − y^2 and z = 4.

Use polar coordinates to find the volume of the given solid.
Under the paraboloid
z = x2 + y2
and above the disk
x2 + y2 ≤ 25

Find the volume enclosed by the cone
x2 +
y2 =
z2
and the plane
3z − y − 3 = 0.
(Round your answer to four decimal places.)

Use a triple integral to find the volume of the solid enclosed
by the paraboloids y=x2+z2 and
y=50−x2−z2.

Use a double integral in polar coordinates to find the volume of
the solid bounded by the graphs of the equations.
z = xy2, x2 + y2 =
25, x>0, y>0, z>0

Find the volume of the solid using a triple
integral.
The solid enclosed between the surfaces x = y2 +
z2 and x = 1 - y2.

Let D be the region enclosed by the cone z =x2 + y2 between the
planes z = 1 and z = 2.
(a) Sketch the region D.
(b) Set up a triple integral in spherical coordinates to ﬁnd the
volume of D.
(c) Evaluate the integral from part (b)

Use a triple integral in cylindrical coordinates to find the
volume of the sphere x^2+ y^2+z^2=a^2

use
cylindrical coordinates: A cylindrical hole of radius a is bored
through the center of a solid sphere of radius 2a. Find the volume
of the hole.

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