15 -15-15 10 08:10 -10 10 15 15 14 13 12 11 10 Find the surface area of the portion of the semi cone z = and z= 16. x2 + y² that lies between the planes z = 8
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- A). Use Pappus's theorem for surface area and the fact that the surface area of a sphere of radius d is 4pid^2 to find the centroid of the semicircle x=(d^2-y^2)^0.5find a parametrization of the surface. The first-octant portion of the cone z = sqrt(x2 + y2)/2 between the planes z = 0 and z = 3 . Cone frustum The portion of the cone z = 2sqrt(x2 + y2) between the planes z = 2 and z = 4Find the volumes of the solids The solid lies between planes perpendicular to the x-axis at x = 0 and x = 1. The cross-sections perpendicular to the x-axis between these planes are circular disks whose diameters run from the parabola y = x2 to the parabola y = √x.
- find a parametrization of the surface. (There aremany correct ways to do these, so your answers may not be the sameas those in the back of the text.) The portion of the cylinder y2 + z2 = 9 between the planes x = 0 and x = 3ntegrate G(x, y, z) = x + y + z over the portion of the plane 2x + 2y + z = 2 that lies in the first octant.Find the volumes of the solids The solid lies between planes perpendicular to the x-axis at x = 0 and x = 6. The cross-sections between these planes are squares whose bases run from the x-axis up to the curve x1/2 + y1/2 = √6.
- A solid has the following properties. When illuminated by rays parallel to the z-axis, its shadow is a circular disk. If the rays are parallel to the y-axis, its shadow is a square. If the rays are parallel to the x-axis, its shadow is an isosceles triangle. Assume that the projection onto the xz plane is a square whose sides have length 1. a) What is the volume of the largest such solid? b) Is there a smallest such volume? Explain.find the volume The solid lies between planes perpendicular to the x-axis at x = -1 and x = 1. The cross-sections perpendicular to the x-axis betwwen these planes are squares whose bases run from the semicircle y = -sqrt(1 - x2) to the semicircle y = sqrt(1 - x2).ntegrate G(x, y, z) = xyz over the surface of the rectangular solid cut from the first octant by the planes x = a, y = b, and z = c.
- Find the volumes of the solids The solid lies between planes perpendicular to the x-axis at x = 0 and x = 1. The cross-sections perpendicular to the x-axis between these planes are circular disks whose diameters run from the parabola y = x2 to the parabola y = sqrt(x).find a parametrization of the surface. The cap cut from the sphere x2 + y2 + z2 = 9 by the cone z = sqrt(x2 + y2) . The portion of the sphere x2 + y2 + z2 = 4 in the first octant between the xy-plane and the cone z = sqrt(x2 + y2).Find the volumes of the solid...................The solid lies between planes perpendicular to the x-axis at x = -1 and x = 1. The cross-sections perpendicular to the x-axis are circular disks whose diameters run from the parabola y = x2 to the parabola y = 2 - x^2.