Question

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

Answer #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...

Describe the given surface
z = sqrt(1-(x^2+y^2))
a. cone b. top half of sphere c. top half of ellipsoid d.
paraboloid

Find the surface area of the portion of the sphere z = sqrt(4 -
x^2 - y^2) that lies between the cylinders x^2 + y^2 = 1 and x^2 +
y^2 = 4

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.

Find the volume found by rotating the region between y=x^2,
y=sqrt(x), about the line y=1

Find the mass of a thin funnel in the shape of a cone
z =
sqrt
x2 + y2
, 1 ≤ z ≤ 4
if its density function is
ρ(x, y, z) = 7 − z.

Let S be the surface given by the part of the sphere x^2 +y^2
+z^2 = 4 that lies below the cone z=−sqrt( x^2+y^2) .
Give a parametric representation of the surface S and determine
the surface area of S

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

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.

For f(x,y,z) = sqrt(35-x^2-4y^2-2z) 1. Find the gradient of
f(x,y,z) 2. Evaluate delta f(x,y,z) 3. Find the unit vectors U+ and
U- , that give the direction of steepest ascent and the steepest
descent respectively.

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