E is the solid that lies above the cone z = √√x² + y² and below the sphere x² + y² + z² = z a. Sketch the solid E, with shading. Hint: Complete the square for the sphere (the z- variable) to get the center of the sphere. b. Set up but do not evaluate the integral for the mass of the solid E if the density is proportional to distance from the origin. Use spherical coordinates.

Q: Use cylindrical coordinates. Find the volume of the solid that lies between the paraboloid z = x2 +…

A:

Q: Consider the unit sphere x² + y² + z² = 1. Find the average distance from its north pole to a point…

A: Given: x2+y2+z2=1 It is equation of sphere of radius r=1 unit. We have to find the average distance…

Q: Determine the coordinates of the centroid of the trapezoidal area shown. Assume a = 290 mm, b = 405…

A:

Q: Find the area of the surface. The part of the sphere x² + y² + z² = 36 that lies above the plane z =…

A: Consider the sphere x2+y2+z2=36 For z=3, the projection of the part of the sphere in the xy-plane…

Q: Find the lateral surface area of the part of the cylinder a + y = 1 that lies within the sphere z²…

A:

Q: Let the center of Earth be located at the origin of a sphere O(0, 0, 0), with the positive z-axis…

A: City is located at 36.78°N and 124.44°W. Assume the radius of Earth is 4000 mi.To Find: Express the…

Q: A hemisphere of x? + y? + z2 = a? is shown. A cylinder is placed such the axis of both hemisphere…

A: Surface area is given by ∬D∂z∂x2+∂z∂y2+1dA for a functionz=f(x,y) where D is the projection of the…

Q: 1. Use Stokes' Theorem to find the portion of the sphere x² + y² +2²=5 inside the cylinder z² + y² =…

A:

Q: Evaluate F. dS, where F = 6xy²i + 6x²yj + 2z°k and S is the surface of the unit sphere.

A: