Evaluate the Spherical Coordinate Integral A) $\frac { 7189 } { 48 } \pi$

question 365

Multiple Choice

Evaluate the spherical coordinate integral.
- $$\int _ { 0 } ^ { \pi / 2 } \int _ { 0 } ^ { \pi / 3 } \int _ { \sec \varphi } ^ { 7 } \varrho ^ { 3 } \sin \varphi \mathrm { de } d \varphi \mathrm { d } \theta$$

• A) \(\frac { 7189 } { 48 } \pi\)
• B) \(\frac { 1799 } { 6 } \pi\)
• C) \(\frac { 1799 } { 12 } \pi\)
• D) \(\frac { 7189 } { 24 } \pi\)

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Definitions:

Transform Fault

A type of fault where two tectonic plates slide past one another horizontally, often causing earthquakes.

Lahars

Volcanic mudflows or debris flows composed of a slurry of pyroclastic material, rocky debris, and water, that flow down from a volcano, often following a volcanic eruption.

Basaltic Lava

A type of molten rock that is low in silica and flows easily, typically forming smooth, broad volcanic features.

Shield Volcano

A type of volcano with broad, gently sloping sides, built by the eruption of low-viscosity lava that can flow long distances.