Question

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

Answer #1

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

Use the triple integrals and spherical coordinates to find the
volume of the solid that is bounded by the graphs of the given
equations. x^2+y^2=4, y=x, y=sqrt(3)x, z=0, in first octant.

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.)

Set up a triple integral in cylindrical coordinates to compute
the volume of the solid bounded between the cone z 2 = x 2 + y 2
and the two planes z = 1 and z = 2.
Note: Please write clearly. That had been a big problem for me
lately. no cursive Thanks.

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.

Find the volume of the solid which is bounded by the cylinder
x^2 + y^2 = 4 and the planes z = 0 and z = 3 − y. Partial credit
for the correct integral setup in cylindrical coordinates.

Find the volume of the solid generated by revolving the region
bounded by the graphs of y = e x/4 , y = 0, x = 0, and x = 6 about
the x−axis.
Find the volume of the solid generated by revolving the region
bounded by the graphs of y = √ 2x − 5, y = 0, and x = 4 about the
y−axis.

Use cylindrical coordinates to find the volume of the region
in the first octant bounded by a cylinder ?^2+ ?^2= 9 and a plane
2? + 3? + 4? = 12.

Find the volume of the generated solid when the region
bounded by the graphs of the given equations is rotated around the
y-axis.
y=√x, x = 3y y = 0

Use cylindrical shells to find the volume of the solid obtained
by rotating the region bounded on the right by the graph of
g(y)=9√y and on the left by the y-axis for 0≤y≤8, about the x-axis.
Round your answer to the nearest hundredth position.
V=?

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