Find the center of mass of the solid bounded by the surfaces z =
x ^ 2 + y ^ 2 and z = 8-x ^ 2-y ^ 2. Consider that the density of
the solid is constant equal to 1.
Mass= ?
x=?
y=?
z=?
Step by step please
a. Find the volume of the solid obtained by rotating the region
enclosed by the curves y = 4 x^2 , y = 5 − x^2 about the line y =
11
b. Find the volume of the solid obtained by rotating the region
enclosed by the graphs about the given axis.
y = 2sqt (x), y=x, about x=-20.
Please leave your answer in fraction if
possble
Consider the surfaces x^2 + y^2 + z^2 = 1 and (z +√2)2 = x^2 +
y^2, and let (x0, y0, z0) be a point
in their intersection. Show that the surfaces are tangent at this
point, that is, show that the
have a common tangent plane at (x0, y0, z0).
Find the volume of the solid by subtracting two volumes, the
solid enclosed by the parabolic cylinders
y = 1 − x2, y = x2 − 1 and the planes x +
y + z = 2, 5x + 2y − z + 13 = 0.