Question

(08.05 MC)

Answer 1

Answer:

The rotation of the rectangle, of area 12 squared units, about y-axis produces a cylinder, with a volume of 48$\pi$ 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 = $\pi$$r^{2}$h

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

                V = $\pi$ × $(4)^{2}$ × 3

                   = 48$\pi$ cubic units

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