Use Cylindrical Coordinates to Find the Volume of the Solid $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 256$

question 47

Multiple Choice

Use cylindrical coordinates to find the volume of the solid inside both
$x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 256$ and $( x - 8 ) ^ { 2 } + y ^ { 2 } = 64$ .

• A) \(\frac { 8,192 } { 9 } ( 6 \pi - 7 )\)
• B) \(\frac { 8,192 } { 9 } ( 3 \pi - 4 )\)
• C) \(\frac { 8,192 } { 5 } ( 6 \pi - 7 )\)
• D) \(\frac { 8,192 } { 9 } ( 3 \pi + 4 )\)
• E) \(\frac { 8,192 } { 5 } ( 6 \pi + 7 )\)

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Definitions:

Interval Measures

A scale of measurement where the difference between any two consecutive measures is the same, but it does not have a true zero point, e.g., temperature scales.

Equal Intervals

A measurement scale where the difference between values is the same across the scale.

True Zero

A point on a scale which represents a complete absence of the measured entity, not merely an arbitrary point.

Powerful

Having great control, influence, or effect on others or outcomes.