Find the Volume of the Solid Generated by Revolving the Region

question 145

Multiple Choice

Find the volume of the solid generated by revolving the region about the y-axis.
-The region enclosed by $x = \sqrt { \sin 3 y } , 0 \leq y \leq \frac { \pi } { 6 } , x = 0$

• A) \(3 \pi\)
• B) \(\frac { \pi } { 3 }\)
• C) \(\frac { \pi } { 6 }\)
• D) \(6 \pi\)

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Definitions:

Papillary Layer

The upper layer of the dermis that interdigitates with the epidermis, containing loose connective tissue and forming dermal papillae.

Epidermis

The outermost layer of the skin, providing a waterproof barrier and creating our skin tone, while also offering protection against pathogens.

Dermis

The thick layer of living tissue below the epidermis which forms the true skin, containing sweat glands, hair follicles, and connective tissue.

Hypodermis

The innermost layer of skin, consisting of fat and connective tissues that provide insulation and cushioning to the body.