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Single Var Calculus -- Volumes of Revolution
consider the curves y = 6 x = 0 and y = x2+2
Revolve the bound area around the y-axis and find the volume of the product solid.
Here's what I did.
r = x = (y - 2)1/2
V = pi * INTEGRAL from y = 2 -> y = 6 of r2 dy = y - 2 dy = y2/2 - 2y from 6 - > 2 = 8pi
All of my calculations are correct, but I am not sure if i selected the radius of the solid correctly. This is why i chose to do this problem -- I need to get better at figuring out what the radius of the solid will be.
Did I choose it correctly? If not, what is correct, and is there any good way to check yourself to see if you did indeed chose your radius correctly?
consider the curves y = 6 x = 0 and y = x2+2
Revolve the bound area around the y-axis and find the volume of the product solid.
Here's what I did.
r = x = (y - 2)1/2
V = pi * INTEGRAL from y = 2 -> y = 6 of r2 dy = y - 2 dy = y2/2 - 2y from 6 - > 2 = 8pi
All of my calculations are correct, but I am not sure if i selected the radius of the solid correctly. This is why i chose to do this problem -- I need to get better at figuring out what the radius of the solid will be.
Did I choose it correctly? If not, what is correct, and is there any good way to check yourself to see if you did indeed chose your radius correctly?
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