Math Problem Statement
Set up triple integrals for the volume of the sphere
rhoρequals=55
in
Bold a.a.
spherical,
Bold b.b.
cylindrical, and
Bold c. rectangularc. rectangular
Solution
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Math Problem Analysis
Mathematical Concepts
Multivariable Calculus
Triple Integrals
Coordinate Systems
Spherical Coordinates
Cylindrical Coordinates
Rectangular Coordinates
Formulas
Volume element in spherical coordinates: dV = ρ^2 sin(φ) dρ dθ dφ
Volume element in cylindrical coordinates: dV = r dz dr dθ
Volume element in rectangular coordinates: dV = dx dy dz
Equation of the sphere: x^2 + y^2 + z^2 = 25
Theorems
Jacobian determinant for coordinate transformations
Suitable Grade Level
Undergraduate - Calculus III
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