Question

Volume of Concrete A culvert is constructed out of large cylindrical shells cast in concrete, as shown in the figure. Using the formula for the volume of a cylinder given on the inside front cover of this book, explain why the volume of the cylindrical shell is $$V=\pi R^{2} h-\pi r^{2} h$$ Factor to show that $V=2 \pi \cdot$ average radius $\cdot$ height $\cdot$ thickness Use the unrolled diagram to explain why this makes sense geometrically.

Name: volume of concrete a culvert is constructed out of large cylindrical shells cast in concrete as shown in the figure using the formula for the volume of a cylinder given on the inside front cover of 2
Uploaded: 2020-03-17T17:29:43-08:00
Duration: 2 min 23 s
Channel: Heather Zimmers
Description: volume of concrete a culvert is constructed out of large cylindrical shells cast in concrete as shown in the figure using the formula for the volume of a cylinder given on the inside front cover of 2

          Volume of Concrete A culvert is constructed out of large
cylindrical shells cast in concrete, as shown in the figure.
Using the formula for the volume of a cylinder given on the
inside front cover of this book, explain why the volume of
the cylindrical shell is
$$V=\pi R^{2} h-\pi r^{2} h$$
Factor to show that
$V=2 \pi \cdot$ average radius $\cdot$ height $\cdot$ thickness
Use the unrolled diagram to explain why this makes sense
geometrically.

Added by Richard A.

College Algebra

James Stewart, Lothar Redlin, Saleem… 7th Edition

Chapter 0

Instant Answer

Solved by Expert Heather Zimmers

03/17/2020

Step 1

Step 1: Start with the formula for the volume of a cylindrical shell: $V = \pi R^{2} h - \pi r^{2} h$. Show more…

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Volume of Concrete A culvert is constructed out of large cylindrical shells cast in concrete, as shown in the figure. Using the formula for the volume of a cylinder given on the inside front cover of this book, explain why the volume of the cylindrical shell is $$V=\pi R^{2} h-\pi r^{2} h$$ Factor to show that $V=2 \pi \cdot$ average radius $\cdot$ height $\cdot$ thickness Use the unrolled diagram to explain why this makes sense geometrically.