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ehgdhjahag
15.07.2020 •
Mathematics
Find the volume of the solid generated by revolving the region enclosed by the triangle with vertices (1 comma 0 ), (3 comma 2 ), and (1 comma 2 )about the y-axis. Use the washer method to set up the integral that gives the volume of the solid.
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Ответ:
Volume =![\frac{20\pi }{3}](/tpl/images/0706/1796/d2299.png)
Step-by-step explanation: The washer method is a method to determine volume of a solid formed by revolving a region created by any 2 functions about an axis. The general formula for the method will be
V =![\pi \int\limits^a_b {(R(x))^{2} - (r(x))^{2}} \, dx](/tpl/images/0706/1796/ed283.png)
For this case, the region generated by the conditions proposed above is shown in the attachment.
Because it is revolting around the y-axis, the formula will be:
Since it is given points, first find the function for points (3,2) and (1,0):
m =
= 1
y - 0 = 1(x-1)
y = x - 1
As it is rotating around y:
x = y + 1
This is R(y).
r(y) = 1, the lower limit of the region.
The volume will be calculated as:
The volume of the region bounded by the points is
.
Ответ:
n²=196
n=√196, or 14
Then P=4(14)=56 meters
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