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Use cylindrical coordinates to find the volume of the solid. Solid inside both x2 + y2 + z2 - 16 and (x - 2)2 + y2-4 Use cylindrical coordinates to find the volume of the solid. Solid inside both x2 + y2 + z2 - 16 and (x - 2)2 + y2-4
please show all your steps. 4. Conpute the volume of the region s inside the cylinder z2 +y2 = 1, between the paraboloid :-x2 + y2-2 and the plane z + :-4 4. Conpute the volume of the region s inside the cylinder z2 +y2 = 1, between the paraboloid :-x2 + y2-2 and the plane z + :-4
orientation. Find the volume of the piece of the sphere x2 + y2 + z2-1 which lies both inside the cylinder x2 + y2-1/2 and inside the first coordinate octant (that is, x,y,z 2 0). 4. 5. For the vector field F (2x(y +2)-y2-Z2), what is the surface integral of this field over the unit-radius
Find the volume inside both x^2+y^2+z^2=1 and x^2+y^2=x. Q4 (10 points) Find the volume inside both x2 + y2 + z2 = 1 and x2 + y2 = x.
Use spherical coordinates: 36) Find the volume of the solid outside the cone z2 = x2 + y2 and inside the sphere x2 + y2 + z2 1. Sketch the drawing of the graph. Use spherical coordinates: 36) Find the volume of the solid outside the cone z2 = x2 + y2 and inside the sphere x2 + y2 + z2 1. Sketch the drawing of the graph.
Problem 4- Compute the volume of the solid inside the sphere x2 + y2 + z2 = R2 between the two planes z = a and z = b where () < a < b < R.
2. (20 pts) Find the surface area of that part of the sphere x2 + y2 + z2-4 that lies inside the paraboloid z x2 + y2. 2. (20 pts) Find the surface area of that part of the sphere x2 + y2 + z2-4 that lies inside the paraboloid z x2 + y2.
Find the volume of the solid bounded on top by sphere x2+y2+z2= 9 , on the bottom by the plane z = 0, around the side by the cylinder x2+y2= 4.
Use spherical coordinates. Find the volume of the solid that lies within the sphere x2 + y2 + z2 = 4, above the xy-plane, and below the cone z =√( x2 + y2)
2: (a) Find all solutions (x, y) = Z2 to Pell's Equation x2 – 29 y2 = 1. (b) Find all solutions (x, y) € Z to the Pell-like equation x2 - 21 y2 = 4.