(08.05 MC)
The coordinates A(0,0), B(0, 3), C(4,3) and D(4,0) are graphed and connected together.
What 3-dimensional shape will be created when this shape is rotated about the y-axis?
Provide an explanation and proof for your answer to receive full credit. (5 points)
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The rotation of the rectangle, of area 12 squared units, about y-axis produces a cylinder, with a volume of 48 cubic units.

Step-by-step explanation:

Rotation about x-axis or y-axis at an angle requires some general rules. When a 2D figure is rotated about a line a 3d figure would be produced. This can be done through a process called solid of revolution.

From the question, connecting the given coordinates produces a rectangle with a length of 4 units and width 3units.

Area of the rectangle = Length × width

                                   = 4 × 3

                                   = 12 square units

The required rule for rotation of a figure about y-axis is: (x, y) → (-y, x).

If the given rectangle is rotated about y-axis, a cylinder would be formed.

The volume of the cylinder = V = h

where: r = 4 units and h = 3 units.

                V = × × 3

                   = 48 cubic units

Therefore, the rotation of the rectangle of area 12 squared units produces a cylinder with volume of 48 cubic units.

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step-by-step explanation: