Physics Technology Update (4th Edition)

Published by Pearson
ISBN 10: 0-32190-308-0
ISBN 13: 978-0-32190-308-2

Chapter 1 - Introduction to Physics - Problems and Conceptual Exercises - Page 16: 36

Answer

$10^{5}~seats$

Work Step by Step

Imagine two concentric circles of radius $r_{1}=60~m$ and $r_{2}=80~m$. The seats are in the region between the circumferences of the circles. We estimate that there are five seats per $m^{2}$. Let $A_{1}$ be the area of the circle 1, $A_{2}$ be the area of the circle 2 and $A$ the area between the circumferences of the circles: $A=A_{2}-A_{1}=π(r_{2})^{2}-π(r_{1})^{2}=π[(80~m)^{2}-(60~m)^{2}]\approx8800~m^{2}$ $8800~m^{2}=(8800~m^{2})(\frac{5~seats}{1~m^{2}})=44,000~seats=4.4\times10^{4}\approx10^{5}~seats$. Notice that $4.4\gt\sqrt 10$.
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