la + 6x + 16, x = 0, and yThe region bounded by f(x)the volume of the solid of revolution.0 is rotated about the y-axis. FindFind the exact value; write answer without decimals.Add WorkSubmit Question

Answered: The region bounded by f(r) la + 6x +…

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 40E: Find the exact volume of the solid that results when the region bounded in quadrant I by the axes...

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Question

la + 6x + 16, x = 0, and y
The region bounded by f(x)
the volume of the solid of revolution.
0 is rotated about the y-axis. Find
Find the exact value; write answer without decimals.
Add Work
Submit Question

Expert Solution

Step 1

$s o l u t i o n : - t h e r e g i o n b o u n d e d b y f (x) = - x^{2} + 6 x + 16, x = 0 a n d y = 0 r o t a t i n g a b o u t t h e y - a x i s u \sin g c y l i n d r i c a l s h e l l m e t h o d r = x h = - x^{2} + 6 x + 16 w h e r e, r = r a d i u s o f c y l i n d r i c a l s h e l l h = h e i g h t / l e n g t h o f c y l i n d r i c a l s h e l l$