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Section 12.5: Problem 7 (1 point) Find the volume of the solid enclosed by the paraboloids z = 25 (x + y ) and z
Section 12.5: Problem 7 (1 point) Find the volume of the solid enclosed by the paraboloids z = 25 (x + y ) and z = 2 - 25 (a2 + ?).Equation of parabobid given in the question . 2 = 25 (x 2 + 12 ) and 2 2 - 25 ( 2 2 +y ) Now, commenting in polan coordinates ie in terms of r and o. hence, 2 2 +y ? = r 2 and drydy = rdrdo so, the equation of paraboloid are:- 2 = 2572 and Z = 2- 25 2 ( ii ) Now, as r is distance from the origin in polar form so it can't be negative. Equating ( 1 ) & ( i ) : - 25 72 2 2- 2572 50 72 = 2 V 2 1 / 5 As 8 1 5 52 distance * can't be negative . Now, perform tripple integration for volume.. 2 1 ie , 1 2 :2 - 25 72 V = - r dz drdo D= 0 1 2 = 25 1 2 rest is similar in accordance to me last solution
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