Solve the Problem $D$ Be the Region Bounded Below by The $x y$

question 24

Multiple Choice

Solve the problem.
-Let $D$ be the region bounded below by the $x y$ -plane, above by the sphere $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 49$ , and on the sides by the cylinder $x ^ { 2 } + y ^ { 2 } = 36$ . Set up the triple integral in cylindrical coordinates that gives the volume of $D$ using the order of integration $\mathrm { dz } \mathrm { dr } \mathrm { d } \theta$ .

• A) \(\int _ { 0 } ^ { 2 \pi } \int _ { 0 } ^ { 7 } \int _ { 0 } ^ { \sqrt { 36 - z ^ { 2 } } } r d z d r d \theta\)
• B) \(\int _ { 0 } ^ { 2 \pi } \int _ { 0 } ^ { 6 } \int _ { 0 } ^ { \sqrt { 49 - z ^ { 2 } } } r d z d r d \theta\)
• C) \(\int _ { 0 } ^ { 2 \pi } \int _ { 0 } ^ { 7 } \int _ { 0 } ^ { \sqrt { 36 - r ^ { 2 } } } r d z d r d \theta\)
• D) \(\int _ { 0 } ^ { 2 \pi } \int _ { 0 } ^ { 6 } \int _ { 0 } ^ { \sqrt { 49 - r ^ { 2 } } } r d z d r d \theta\)

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Definitions:

Steering Knuckles

Components of the suspension system that pivot on ball joints, to which the wheels are attached, allowing the wheels to steer.

Control Arms

Components in a vehicle's suspension system that link the chassis to the wheel hub, facilitating smooth movement and steering.

Ball Joints

Pivotal bearings in a vehicle's suspension system that connect the wheel hubs to the rest of the suspension, allowing for smooth steering and suspension movement.

Upper Steering Pivot

A pivot point in steering mechanisms allowing for the rotation of wheels, essential for vehicle maneuverability.