Use a Spherical Coordinate Integral to Find the Volume of the Given

question 197

Multiple Choice

Use a spherical coordinate integral to find the volume of the given solid.
-the solid between the sphere $\varrho = 1$ and the cardioid of revolution $\varrho = 6 + 4 \cos \varphi$

• A) \(\frac { 622 } { 3 } \pi\)
• B) \(\frac { 1244 } { 3 } \pi\)
• C) \(\frac { 1555 } { 6 } \pi\)
• D) \(\frac { 1555 } { 3 } \pi\)

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Definitions:

Proportional Band

A control parameter in PID controllers that determines the range of proportional action surrounding a setpoint for maintaining system stability.

Factory-Tuned

Refers to equipment or systems that have been pre-set or adjusted at the manufacturing site for optimal performance before delivery.

Proportional Controller

A type of feedback control system that outputs a control signal proportional to the error signal, which is the difference between the desired and actual system states.