Use the method of cylindrical shells to find the volume of the solid obtained by rotating the...
Question:
Use the method of cylindrical shells to find the volume of the solid obtained by rotating the region bounded by {eq}y=8x^{(\frac{1}{2})} \ and \ y=8x^2 {/eq} about the y axis
Volume of Solid of Revolution:
We are told to find the volume of the solid using the cylindrical shell method thus we will be using the formula {eq}V=2\pi \int_{a}^{b}rh\:dr {/eq} where {eq}r {/eq} is the centroid of the region, {eq}h {/eq} is the height and {eq}dr {/eq} is the width.
Answer and Explanation: 1
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From the graph,
{eq}r=x,\:h=y,\:dr=dx {/eq}
Substituting to the formula {eq}V=2\pi \int_{a}^{b}rh\:dr {/eq}
Thus,...
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How to Find Volumes of Revolution With Integration
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Chapter 14 / Lesson 5
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The volume of a revolution can be calculated using the slicing method, the disk method, and the washer method. Explore the processes of the three methods and discover how to use them to find the volumes of revolution.
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