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 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
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