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A rectangle is shown on the coordinate grid with vertices
(0,0),(2,0),(0,3), and
(2,3). A solid is formed by rotating the rectangle about the
x-axis.
Select all true statements about the revolved solid.
The revolved solid is a cylinder with a base radius of 3 units.
The revolved solid is a cylinder with a base radius of 1 unit.
The revolved solid is a cylinder with a height of 2 units.
The revolved solid is a cylinder with a height of 3 units.
The revolved solid is a rectangular prism with a base length of 2 units.
The revolved solid is a rectangular prism with a base length of 4 units.

A rectangle is shown on the coordinate grid with vertices $(0,0),(2,0),(0,3)$ , and $(2,3)$ . A solid is formed by rotating the rectangle about the $x$ -axis. $\newline$ Select all true statements about the revolved solid. $\newline$ The revolved solid is a cylinder with a base radius of $3$ units. $\newline$ The revolved solid is a cylinder with a base radius of $1$ unit. $\newline$ The revolved solid is a cylinder with a height of $2$ units. $\newline$ The revolved solid is a cylinder with a height of $3$ units. $\newline$ The revolved solid is a rectangular prism with a base length of $2$ units. $\newline$ The revolved solid is a rectangular prism with a base length of $4$ units.

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Reflections of functions

Full solution

Q. A rectangle is shown on the coordinate grid with vertices

(0,0),(2,0),(0,3)

, and

(2,3)

. A solid is formed by rotating the rectangle about the

x

-axis.

\newline

Select all true statements about the revolved solid.

\newline

The revolved solid is a cylinder with a base radius of

3

units.

\newline

The revolved solid is a cylinder with a base radius of

1

unit.

\newline

The revolved solid is a cylinder with a height of

2

units.

\newline

The revolved solid is a cylinder with a height of

3

units.

\newline

The revolved solid is a rectangular prism with a base length of

2

units.

\newline

The revolved solid is a rectangular prism with a base length of

4

units.

Identify Dimensions: Identify the dimensions of the rectangle before rotation. $\newline$ The rectangle has vertices at $0,0$ , $2,0$ , $0,3$ , and $2,3$ . This means the rectangle has a width of $2$ units (along the x-axis) and a height of $3$ units (along the y-axis).
Effect of Rotation: Understand the effect of rotating the rectangle about the $x$ -axis. $\newline$ When the rectangle is rotated about the $x$ -axis, the height of the rectangle becomes the radius of the base of the cylinder, and the width becomes the height of the cylinder.
Base Radius Determination: Determine the base radius of the revolved solid. The height of the rectangle ( $3$ units) becomes the radius of the base of the cylinder after rotation.
Height Determination: Determine the height of the revolved solid. $\newline$ The width of the rectangle ( $2$ units) becomes the height of the cylinder after rotation.
Check Statements: Check the statements against the determined dimensions of the revolved solid. $\newline$ The revolved solid is a cylinder with a base radius of $3$ units. (True) $\newline$ The revolved solid is a cylinder with a base radius of $1$ unit. (False) $\newline$ The revolved solid is a cylinder with a height of $2$ units. (True) $\newline$ The revolved solid is a cylinder with a height of $3$ units. (False) $\newline$ The revolved solid is a rectangular prism with a base length of $2$ units. (False, it is not a prism) $\newline$ The revolved solid is a rectangular prism with a base length of $4$ units. (False, it is not a prism)

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\newline

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