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A rectangle is shown on the coordinate grid with vertices
(-3,0),(-1,0),(-3,3), and
(-1,3). A solid is formed by rotating the rectangle about the line
x=-1.
Select all true statements about the revolved solid.
The revolved solid is a cylinder with a base radius of 2 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.
37241931,42870

A rectangle is shown on the coordinate grid with vertices $(-3,0),(-1,0),(-3,3)$ , and $(-1,3)$ . A solid is formed by rotating the rectangle about the line $x=-1$ . $\newline$ Select all true statements about the revolved solid. $\newline$ The revolved solid is a cylinder with a base radius of $2$ 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. $\newline$ $37241931$ , $42870$

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Write equations of hyperbolas in standard form using properties

Full solution

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

(-3,0),(-1,0),(-3,3)

, and

(-1,3)

. A solid is formed by rotating the rectangle about the line

x=-1

.

\newline

Select all true statements about the revolved solid.

\newline

The revolved solid is a cylinder with a base radius of

2

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.

\newline

37241931

,

42870

Identify Dimensions: Identify the dimensions of the rectangle. The rectangle has vertices at $(-3,0)$ , $(-1,0)$ , $(-3,3)$ , and $(-1,3)$ . The length of the rectangle (height of the solid) can be found by subtracting the y-coordinates of the horizontal vertices: $3 - 0 = 3$ units. The width of the rectangle (radius of the base of the solid) can be found by subtracting the x-coordinates of the vertical vertices: $-1 - (-3) = 2$ units.
Determine Radius: Determine the radius of the base of the solid. $\newline$ Since the rectangle is rotated about the line $x=-1$ , the distance from this line to the edge of the rectangle is the radius of the base of the cylinder. The closest $x$ -coordinate of the rectangle to the line $x=-1$ is at $x=-3$ , which is $2$ units away. Therefore, the radius of the base of the cylinder is $2$ units.
Determine Height: Determine the height of the solid. $\newline$ The height of the solid is the same as the length of the rectangle, which we have already determined to be $3$ units.
Identify Shape: Identify the shape of the solid. The solid formed by rotating a rectangle around a line parallel to one of its sides is a cylinder.
Select True Statements: Select all true statements about the revolved solid. $\newline$ Based on the calculations: $\newline$ - The revolved solid is a cylinder with a base radius of $2$ 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 (False). $\newline$ - The revolved solid is a cylinder with a height of $3$ units (True). $\newline$ - 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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