Math Problem Statement
A volume is described as follows:
- the base is the region bounded by x=-y^2+16y-43 and x=y^2-18y+101 ;
- every cross section perpendicular to the y-axis is a semi-circle.
Solution
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Math Problem Analysis
Mathematical Concepts
Volume of solids
Area of semi-circles
Quadratic equations
Definite integrals
Formulas
Quadratic equation formula: ax^2 + bx + c = 0
Diameter of cross-sections: D(y) = (upper curve) - (lower curve)
Area of a semi-circle: A = (1/2)πr^2
Volume of solid: V = ∫A(y) dy
Theorems
Quadratic Formula
Fundamental Theorem of Calculus
Suitable Grade Level
Grades 11-12 (Advanced high school calculus)
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