A dilation of the plane with scaling factor c is a transformation that maps the point (x, y) to the point (cx, cy). Applying a dilation to a region in the plane produces a geometrically similar shape. A manufacturer wants to produce a 5-liter (5000 cm³) terra-cotta pot whose shape is geometrically similar to the solid obtained by rotating the region R₁ shown in the figure about the y-axis.

(a) Find the volume V₁ of the pot obtained by rotating the region R₁.

(b) Show that applying a dilation with scaling factor c transforms the region R₁ into the region R₂.

(c) Show that the volume V₂ of the pot obtained by rotating the region 52 is c³V₁.

(d) Find the scaling factor c that produces a 5-liter pot.

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y4 (cm) y4 (cm) y = 8c y= 8 R2 y=x y=x/c? |y=1 y=c x (ст) x (cm)