College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter 3 - Summary, Review, and Test - Review Exercises - Page 438: 82



Work Step by Step

Since the exercise says that the volume of a pyramid varies JOINTLY as its height and area of the base, we can express this in the following manner: $$V_{pyramid} = khA_{base}$$ where $V$ is the volume of the pyramid, $h$ is the height of the pyramid, $A$ is the area of the base of the pyramid and $k$ is a proportionality constant. Since we know that, when $h=15$ and $A=35$, $V=175$, we can calculate $k$ as so: $$V = khA$$ $$\frac{V}{hA} = k$$ $$\frac{(175)}{(15)(35)} = k = \frac{1}{3}$$ and, finally, we can answer the question: $$V = \frac{1}{3}(20)(120)$$ $$V = 800$$
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