Use the shell method to find the volume of the solid generated by revolving the region bound by ...
Question:
Use the shell method to find the volume of the solid generated by revolving the region bound by {eq}y = x^2+4, x=0, y=9 {/eq} about the y-axis.
Volume of the Solid :
To find the volume of the solid obtained by rotating the region bounded by the curves first we find the point of intersection of the curves. The point of intersection of the two curves is as follows
{eq}x=1\Rightarrow y=1\\ x=2\Rightarrow y=4 {/eq}
Therefore, the points of intersection are (1,1) and (2,4). If the region under the curve {eq}y=f(x) {/eq} on the interval {eq}\left [ a,b \right ]{/eq} then the volume of the solid obtained by revolving {eq}R {/eq} about the y-axis is as follows
{eq}\mathbf{Volume}=2\pi\int_{a}^{b}r\: h\: dx {/eq}
Where, {eq}r {/eq} is radius of the solid and {eq}h {/eq} is the height of the solid.
Answer and Explanation: 1
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View this answerConsider the curves
{eq}y = x^2+4, x=0, y=9,\: \, {/eq}
about the y- axis that is {eq}x=0 {/eq}
The point of intersection of the two curves is as...
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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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