Question

Find the volume of the solid bounded by the cylinder x^2+y^2=9 and the planes z=-10 and 1=2x+3y-z

Answer #1

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 bounded by the cylinder x 2 + y 2
= 1, the paraboloid z = x 2 + y 2 , and the plane x + z = 5

draw the solid bounded above z=9/2-x2-y2
and bounded below x+y+z=1. Find the volume of this
solid.

Find the integral that represents the volume of the solid
bounded by the planes y = 0, z = 0, y = x and 6x + 2y + 3z = 6
using double integrals.

Find the integral that represents the volume of the solid
bounded by the planes y = 0, z = 0, y = x, and 6x + 2y + 3z = 6. No
need to solve the integral.

Find the volume of the solid bounded by the surface z=
5+(x-y)^2+2y and the planes x = 3, y = 3 and coordinate planes.
a. First, find the volume by actual calculation.
b. Estimate the volume by dividing the region into nine equal
squares and evaluating the functional value at the mid-point of the
respective squares and multiplying with the area and summing it.
Find the error from step a.
c. Then estimate the volume by dividing each sub-square above...

The volume of the object bounded by z = 0, z = x
planes and x = 2 -y * 2 parabolic cylinder is which of the
following?

4. Consider the solid bounded by the paraboloid x^2+ y^2 + z = 9
as well as by the planes y = 3x and z = 0 in the first octant.
(a) Graph the integration domain D.
(b) Calculate the volume of the solid with a double
integral.

F(x, y, z) =< 3xy^2 , xe^z , z^3 >, S is the solid bounded
by the cylinder y2 + z2 = 1 and the planes x
= −1 and x = 2 Find he surface area using surface integrals. DO NOT
USE Divergence Theorem. Answer: 9π/2

Use triple integration to find the volume of the solid cylinder
x^2 + y^2 = 9 that lies above z = 0 and below x + z = 4.

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