Correct, except you forgot to distribute the 1/2 back into the integral, so the correct answer is actually pi/2
5. Find the volume of the region enclosed on the top by the plane z =...
1 point) Find the volume of the wedge-shaped region (Figure 1) contained in the cylinder x2 + y2-4 and bounded above by the plane z = x and below by the xy-plane. z=x FIGURE 1
1 point) Find the volume of the wedge-shaped region (Figure 1) contained in the cylinder x2 + y2-4 and bounded above by the plane z = x and below by the xy-plane. z=x FIGURE 1
1. (10 points) Find the volume of the solid under the surface z = 1 +x2y2 and above the region of the xy-plane enclosed by x y2 and 1
1. (10 points) Find the volume of the solid under the surface z = 1 +x2y2 and above the region of the xy-plane enclosed by x y2 and 1
The solid S sits below the plane z = 2x + 5 and above the region in the xy-plane where 1 < x2 + y2 = 4 and x + y < 0. The volume of S is:
Find the volume of the region enclosed by the cylinder x2 + y2 = 25 and the planes z = 0 and y + z = 25. The volume is (Type an exact answer, using a as needed.)
(1 point) Find the volume of the region enclosed by the cone z-V2 + y? and the sphere2y222 1. Volume-
(1 point) Find the volume of the region enclosed by the cone z-V2 + y? and the sphere2y222 1. Volume-
(1 point) Find the volume of the region enclosed by z = 1 – y2 and z = y2 – 1 for 0 < x < 39. V =
7. Find the volume of the region in space, the region beneath z = 4x2 + 9y2 and above the rectangle with vertices (0,0), (3,0), (3,2), (0,2) in the xy-plane. Sketch it
7. Find the volume of the region in space, the region beneath z = 4x2 + 9y2 and above the rectangle with vertices (0,0), (3,0), (3,2), (0,2) in the xy-plane. Sketch it
please answer question 3.
1. Find the integral of the function f(x, y, z)xy+2 z over the region enclosed by the planex +y+z 2 2. Find the volume and center of gravity for the solid in the first octant (x 20, y 20, z20) bounded by 3. Find the center of mass for the solid hemisphere centered at the origin with radius a if the density and the coordinate planes z0,y 0, and x0 the parabolic ellipsoid Z-4-r-y. function is...
find the volume of the following D described below.
cylinder whose base is the region between the circle p=cose and r=2cose and whose top lies in the plane z=3-y.
2. Set up and evaluate the volume integral for the region whose base D lies in the first quadrant in the xy plane and whose top is bounded by x + y + z = 4. 3. Find the volume that is enclosed by both the cone z = x2 + y2 and the sphere x2 + y2 + z = 2