Please solve the problem below. Thank you so much!! Find the volume of the solid bounded by the plane z = 0 and the paraboloid z = 9 -.x² - y².SOLUTIONIf we put z = O in the equation of the paraboloid, we get x² + y2 = 9, so the solid lies under the paraboloid and above the circular disk Dgiven by x2 + y² < 9. In polar coordinates D is given by 0

Find the volume of the solid bounded by the plane z = 0 and the paraboloid z = 9 - x2 - y2. SOLUTION If we put z = 0 in the equation of the paraboloid, we get x2 + y2 = 9, so the solid lies under the paraboloid and above the circular disk D given by x2 + y2 s 9. In polar coordinates D is given by 0 srs 3,0 ses 2n. Since 9 - x2 - y2 = 9 -2, the volume is V= x² - y²)dA Video Example ) (9 - 23r dr de (9r - P)dr de If we had used rectangular coordinates instead of polar coordinates, then we would have obtained (9 - x? - y?)dA = (9 – 2 - y) dydx which is not easy to evaluate because it involves finding S(9 - x2,3/2dx

Find the volume of the solid bounded by the plane z = 0 and the paraboloid z = 9 - x2 - y2. SOLUTION If we put z = 0 in the equation of the paraboloid, we get x2 + y2 = 9, so the solid lies under the paraboloid and above the circular disk D given by x2 + y2 s 9. In polar coordinates D is given by 0 srs 3,0 ses 2n. Since 9 - x2 - y2 = 9 -2, the volume is V= x² - y²)dA Video Example ) (9 - 23r dr de (9r - P)dr de If we had used rectangular coordinates instead of polar coordinates, then we would have obtained (9 - x? - y?)dA = (9 – 2 - y) dydx which is not easy to evaluate because it involves finding S(9 - x2,3/2dx

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 37E: Find the exact volume of the solid that results when the triangular region with vertices at 0, 0, 5,...

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