Semi circle cross sections of a solid help
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Semi circle cross sections of a solid help

[From: ] [author: ] [Date: 12-02-21] [Hit: ]
the x axis, and the y-axis. if the cross sections of s perpendicular to the x-axis are semicircles, then what is the volume of s?how do i figure this out?at the point A(x,......
how do i find this integral?
the base of a solid S is the region enclosed by the graph of 4x+5y=20, the x axis, and the y-axis. if the cross sections of s perpendicular to the x-axis are semicircles, then what is the volume of s?

how do i figure this out?

-
The area of semicircle is πr^2/2

The radius r of semicircle
perpendicular to the x-axis
at the point A(x,0) is
r=[(20-4x)/5]/2=(10-2x)/5

The area of semicircle is

A(x)=π*r^2/2=(2π/25)(5-χ)^2

So V=∫A(x)dx (x=0 to 5)

=10π/3
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