FInd the volume of the solid
Favorites|Homepage
Subscriptions | sitemap
HOME > > FInd the volume of the solid

FInd the volume of the solid

[From: ] [author: ] [Date: 12-10-31] [Hit: ]
The outer radius of the washer will be 2-1/2x and the inner radius will be 2-sqrt(x).The area function A(x) = π [(2-1/2x)^2 - (2-sqrt(x))^2] (i.e.,......
The region between the graphs of x=y^2 and x=2y is rotated around the line y=2.
The volume of the resulting solid is ? Please show a step by step solution. Thank you

-
I'll use the washer method and integrate with respect to x. First if you draw a graph the two functions, you'll see that they intercept at x=0 and x=4. These will be the limits of integration.

The outer radius of the washer will be 2-1/2x and the inner radius will be 2-sqrt(x).
The area function A(x) = π [(2-1/2x)^2 - (2-sqrt(x))^2] (i.e., because the area of a circle is πr^2)
Expanding this yields: π [x^2/4 - 3x +4*sqrt(x)] (you could have integrate the above but I find it easier to expand first to get simple terms)

So V= ∫ A(x)dx between x=0 and x=4 or
=π [x^3/12 - 3x^2/2 + 8x^(3/2)/3] between 4 and zero or
=π [64/12 - 48/2 + 64/3] = 8π/3
1
keywords: solid,the,volume,FInd,of,FInd the volume of the solid
New
Hot
© 2008-2010 http://www.science-mathematics.com . Program by zplan cms. Theme by wukong .