Use Cylindrical Coordinates to Evaluate $\int _ { - 2 } ^ { 2 } \int _ { 0 } ^ { \sqrt { 4 - x ^ { 2 } } } \int _ { 0 } ^ { \sqrt { 16 - x ^ { 2 } - y ^ { 2 } } } z d z d y d x$

question 139

Multiple Choice

Use cylindrical coordinates to evaluate $\int _ { - 2 } ^ { 2 } \int _ { 0 } ^ { \sqrt { 4 - x ^ { 2 } } } \int _ { 0 } ^ { \sqrt { 16 - x ^ { 2 } - y ^ { 2 } } } z d z d y d x$ .
Select the correct answer.

• A) \(12 \pi\)
• B) \(112 \pi\)
• C) \(\frac { 3 } { 2 } \pi\)
• D) \(14 \pi\)

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Definitions:

Axle

A rod or bar on which wheels turn or the housing that supports wheel assemblies. Also used to describe the shaft that transmits drive torque to the drive wheels.

Drivelines

Components, including the driveshaft, axles, CV joints, and differential, that transmit power from the engine to the wheels of a vehicle.

Torque Transfer

The process of transferring rotational force from one part of a mechanical system to another, allowing for movement and work to be done.

U-joints

Universal joints, flexible couplings that allow different parts of a drivetrain to pivot or rotate, accommodating changes in angle or alignment.