Question

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 back 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 Wise the "unrolled" diagram to explain why this makes sense Eeometrically. CAN'T COPY THE GRAPH

          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 back 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
Wise the "unrolled" diagram to explain why this makes sense Eeometrically.
CAN'T COPY THE GRAPH

Added by Christopher J.

Precalculus with Limits

Ron Larson 2nd Edition

Instant Answer

Solved by Expert Sheryl Ezze

09/07/2022

Step 1

The formula is given as $V = \pi R^2 h$, where $R$ is the radius of the base of the cylinder and $h$ is the height of the cylinder. In the case of the culvert, we have a cylindrical shell, which means it is hollow inside. The culvert is made up of two cylinders - Show more…

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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 back 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.