Question

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

Answer #1

hence, V = 4/3 (pi ×
a^{3}) ....volume of sphere of radius a

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

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.

Find the volume of the solid using triple integrals. The solid
region Q cut from the sphere x^2+y^2+z^2=4 by the cylinder r=2sinϑ.
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
Cylindrical coordinates. Evaluate the iterated integral

write and evaluate the triple integral for the function f(x,y,z)
= z^2 bounded above by the half-sphere x^2+y^2+z^2=4 and below by
the disk x^2+y^4=4. Use spherical coordinates.

1)
Use triple integration to find the volume of a sphere with
radius 5 in cylindrical, spherical, and cartesian coordinates.
Evaluate them all.

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.

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

7. Given The triple integral E (x^2 + y^2 + z^2 ) dV where E is
bounded above by the sphere x 2 + y 2 + z 2 = 9 and below by the
cone z = √ x 2 + y 2 . i) Set up using spherical coordinates. ii)
Evaluate the integral

Write down a cylindrical coordinates integral that gives the
volume of the solid bounded above by z = 50 − x^2 − y^2 and below
by z = x^2 + y^2 . Evaluate the integral. (Hint: use the order of
integration dz dr dθ.)

Use cylindrical coordinates.
Find the volume of the solid that is enclosed by the cone
z =
x2 + y2
and the sphere
x2 + y2 + z2 = 128.

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 2 minutes ago

asked 3 minutes ago

asked 9 minutes ago

asked 11 minutes ago

asked 12 minutes ago

asked 28 minutes ago

asked 40 minutes ago

asked 46 minutes ago

asked 59 minutes ago

asked 59 minutes ago

asked 1 hour ago

asked 1 hour ago