Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 1 - Section 1.7 - Modeling with Equations - 1.7 Exercises - Page 80: 87

Answer

Pile is about $7.52ft$ high.

Work Step by Step

The diameter and height have constant connection, which means that for any given time if height = $h$ diameter is $3h$. So, the radius of conical pile is $1.5h$ Volume of a cone is: $V=\frac{\pi r^2 h}{3}$ $1000=\frac{\pi \times 2.25h^2 \times h}{3}$ $3000=2.25\pi h^3$ $h^3\approx 424.41$ $h\approx 7.51501\approx 7.52ft$
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