Solve the Problem $( x - 6 ) ^ { 2 } + y ^ { 2 } \leq 1$

question 189

Multiple Choice

Solve the problem.
-The disk $( x - 6 ) ^ { 2 } + y ^ { 2 } \leq 1$ is revolved about the $y$ -axis to generate a torus. Find its volume. (Hint: $\int _ { - 1 } ^ { 1 } \sqrt { 1 - y ^ { 2 } } d y = \frac { 1 } { 2 } \pi$ , since it is the area of a semicircle of radius 1 .)

• A) \(3 \pi ^ { 2 }\)
• B) \(6 \pi\)
• C) \(12 \pi ^ { 2 }\)
• D) \(6 \pi ^ { 2 }\)

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Definitions:

Vascular Cylinder

The central part of a plant's root system that contains the plant's vascular tissue, including xylem and phloem, for water and nutrient transport.

Casparian Strip

A band of cell wall material in the roots of plants that is impervious to water and solutes, controlling the flow into the vascular system.

Endodermis

The endodermis is the innermost layer of cells in the root cortex of plants, serving as a selective barrier that regulates the flow of water and nutrients from the soil into the vascular system.

Vascular Cylinder

The central part of a root or stem containing the plant's vascular tissue, including xylem and phloem, responsible for water and nutrient transport.