Find the Volume of the Solid Obtained by Rotating the Region

question 72

Short Answer

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis.
$$y = 5 \left( x ^ { 2 } + 4 \right) , y = 5 \left( 12 - x ^ { 2 } \right) ; \text { about } y = - 5$$

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Definitions:

Molluscs

Invertebrates including squids, clams, snails, and chitons; characterized by a visceral mass, a mantle, and a foot.

Visceral Mass

Internal organs of an organism; typically includes components of the digestive, reproductive, and urinary systems (if present).

Mantle

In mollusks, an extension of the body wall that covers the visceral mass and may secrete a shell.

Mollusca

A large phylum of invertebrate animals that includes snails, slugs, mussels, and octopuses, characterized by a soft body that in many species is enclosed by a hard shell.