2. (a) Set up an integral in Cartesian coordinates to find the volume of the solid that lies between the xy- plane and the paraboloid z = 25-2-2. (b) Set up an integral in polar coordinates to find the same volume described above. (c) Set up an integral to find the surface area of the part of the paraboloid z = 25-2-y² that lies above the xy-plane. (You choose which coordinate system to use for this.)

Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter10: Analytic Geometry
Section10.1: The Rectangular Coordinate System
Problem 41E: Find the exact lateral area of each solid in Exercise 40. Find the exact volume of the solid formed...
Question
2. (a) Set up an integral in Cartesian coordinates to find the volume of the solid that lies between the xy-
plane and the paraboloid z = 25-2-2.
(b) Set up an integral in polar coordinates to find the same volume described above.
(c) Set up an integral to find the surface area of the part of the paraboloid z = 25-2-y² that lies
above the xy-plane. (You choose which coordinate system to use for this.)
Transcribed Image Text:2. (a) Set up an integral in Cartesian coordinates to find the volume of the solid that lies between the xy- plane and the paraboloid z = 25-2-2. (b) Set up an integral in polar coordinates to find the same volume described above. (c) Set up an integral to find the surface area of the part of the paraboloid z = 25-2-y² that lies above the xy-plane. (You choose which coordinate system to use for this.)
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