Find the Volume of the Described Solid $x ^ { 2 } + y ^ { 2 } \leq 4$

question 56

Multiple Choice

Find the volume of the described solid.
-The base of the solid is the disk $x ^ { 2 } + y ^ { 2 } \leq 4$ . The cross sections by planes perpendicular to the $y$ -axis between $y = - 2$ and $y = 2$ are isosceles right triangles with one leg in the disk.

• A) \(\frac { 64 } { 3 }\)
• B) \(\frac { 16 } { 3 }\)
• C) \(\frac { 80 } { 3 }\)
• D) \(\frac { 128 } { 3 }\)

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Definitions:

Psoas Minor

A small muscle located in the lower back that helps with flexion of the lumbar spine, though it is absent in a significant portion of the population.

Iliac Crest

The upper margin of the iliac bones, which forms the prominent part of the pelvic hip bone.

Lower Lumbar

Referring to the lower part of the lumbar region of the back, which includes the lower vertebrae of the spine.

Quadratus Lumborum

A muscle in the lower back that helps with the movement of the spine as well as stabilizes the pelvis.