A dilation of the plane with scaling factor c is a transformation that maps the point (x,

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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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Calculus Early Transcendentals

ISBN: 9781337613927

9th Edition

Authors: James Stewart, Daniel K. Clegg, Saleem Watson, Lothar Redlin

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