Answer:
The rotation of the rectangle, of area 12 squared units, about y-axis produces a cylinder, with a volume of 48[tex]\pi[/tex] 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 = [tex]\pi[/tex][tex]r^{2}[/tex]h
where: r = 4 units and h = 3 units.
V = [tex]\pi[/tex] × [tex](4)^{2}[/tex] × 3
= 48[tex]\pi[/tex] cubic units
Therefore, the rotation of the rectangle of area 12 squared units produces a cylinder with volume of 48[tex]\pi[/tex] cubic units.
