(a) Find the volume V inside the cylinder x 2. +y" = = 16, cut off above and below by a hyperboloid of 2 sheets 2 = = x² + y²+49. Evaluate the volume V using polar coordinates .b V = = s = La² L² f dr de. Enter the limits of the double integral, separated by a comma, a, b, c, d = 0,2*Pi,0,4 Enter the integrand f=2*r*sqrt(r^2+49) The volume V = (b) Calculate the volume V bounded by the planes z = 12 - 2x - 3y and z = (12-2x-3y) in the first octant i.e., x 0, y≥ 0, z ≥ 0, The volume V =

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...
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(a) Find the volume V inside the cylinder x 2.
+y" = = 16, cut off above and below by a hyperboloid of 2 sheets
2
=
= x² + y²+49. Evaluate the volume V using polar coordinates
.b
V = = s
= La² L²
f dr de.
Enter the limits of the double integral, separated by a comma,
a, b, c, d = 0,2*Pi,0,4
Enter the integrand
f=2*r*sqrt(r^2+49)
The volume V
=
(b) Calculate the volume V bounded by the planes z = 12 - 2x - 3y and z = (12-2x-3y) in the first octant
i.e., x 0, y≥ 0, z ≥ 0,
The volume V =
Transcribed Image Text:(a) Find the volume V inside the cylinder x 2. +y" = = 16, cut off above and below by a hyperboloid of 2 sheets 2 = = x² + y²+49. Evaluate the volume V using polar coordinates .b V = = s = La² L² f dr de. Enter the limits of the double integral, separated by a comma, a, b, c, d = 0,2*Pi,0,4 Enter the integrand f=2*r*sqrt(r^2+49) The volume V = (b) Calculate the volume V bounded by the planes z = 12 - 2x - 3y and z = (12-2x-3y) in the first octant i.e., x 0, y≥ 0, z ≥ 0, The volume V =
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