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Solutions to Homework 9 - Michigan State University Section 12 7 # 34: Set up an integral in spherical coordinates which computes the volume of the region bounded below by the hemisphere = 1, z 0, and above by the cardioid of revolution = 1 + cos
Triple Integrals in Cylindrical and Spherical Coordinates - NITK Let D be the region bounded below by the cone z = px2 + y2 and above by the paraboloid z = 2 x2 y2: Set up the triple integrals in cylindrical coordinates that give the volume of D using the following orders of integration
Find the volume of the solid above the cone $z=\\sqrt{x^2+y^2}$ and . . . I actually have found the solution using double integral in polar coordinate However, I am curious about whether I could find the same exact solution using triple integral in spherical coordinates but it does not match the one I got from using the double integral
Find the Volume of the Paraboloid X 2 + Y 2 = 4 Z Cut off by the Plane . . . Find the volume of the paraboloid x 2 + y 2 = 4 z cut off by the plane 𝒛=𝟒 Paraboloid : x 2 + y 2 = 4 z Plane : 𝒛=𝟒 Cartesian coordinate → cylindrical coordinates (𝒙,𝒚,𝒛) → (𝒓,𝜽,𝒛) Put 𝒙=𝒓𝒄𝒐𝒔 𝜽 ,𝒚=𝒓𝒔𝒊𝒏 𝜽 ,𝒛=𝒛 ∴ x 2 + y 2 = r 2 ∴ Paraboloid : r 2 =4x and Plane : z = 4
Solved Let D be the region bounded below by the cone z=x2+y2 - Chegg Let D be the region bounded below by the cone z=x2+y2 and above by the paraboloid z=2−x2−y2 Convert the given equations to cylindrical coordinates and then, set up an iterated triple integral for the volume of D in cylindrical coordinates DO NOT evaluate the integral Your solution’s ready to go!