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mikayla62
19.07.2019 •
Mathematics
Consider the region bounded by the curves 2. y = 3 + x , y = 3, and x = 2. find the volume of the solid obtained by rotating this region about the axis y = 3.
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Ответ:
Step-by-step explanation:
Let's look at a point (x,y) on the line y=3+x. The height between (x,y) and the x-axis is y. We want the distance from the axis of rotation which is y=3 so the height (or distance between) point (x,y) on y=3+x and y=3 is y-3.
y-3 is the radius in terms of y.
(3+x)-3=x is the radius in terms of x. I replaced y with 3+x since we have y=3+x.
The area of the circle I drew is![\pi \cdot r^2=\pi \cdot x^2](/tpl/images/0106/6757/961bf.png)
To find the volume we must integrate the area of the circle we found between the bounded lines x=0 and x=2.
Ответ:
109,782/12 = 9148.5
Find 2/3 of that = 6099
The answer is 6099
If this is confusing please ask for more help! :)