Math Problem Statement

Find the volume of the solid obtained by rotating the region in the first quadrant bounded by the given curve about the y-axis. y = 9 - (x - 9)^2

Solution

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Math Problem Analysis

Mathematical Concepts

Calculus
Solid of Revolution
Curve Rotation
Parabolas

Formulas

Volume by Shell Method: V = 2π∫[a,b] x * f(x) dx
Equation of a parabola: y = a(x-h)^2 + k

Theorems

Shell Method for finding volumes of solids of revolution

Suitable Grade Level

Grades 11-12 (Pre-Calculus and Calculus)

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