Revision history [back]

There is a command in Sage to do this, but I do it using my own code.

x,theta=var('x,theta')
def Vol_Rx(f,x,theta,k):
    return([x,-sin(theta)*(f(x)-k),cos(theta)*(f(x)-k)+k])
def Vol_Ry(f,x,theta,k):
    return([(x-k)*cos(theta)+k,sin(theta)*(x-k),f(x)])
f(x)=sqrt(x)
a=0
b=3
p=parametric_plot3d(Vol_Rx(f,x,theta,0),(x,a,b),(theta,0,2*pi))
p+=parametric_plot3d(Vol_Rx(f,x,0,0),(x,a,b),color='red',thickness=3)
show(p)

There Here is a command in the Sage to do this, but command.

revolution_plot3d(sqrt(x),(x,0,3),(0,2*pi),show_curve=True,parallel_axis='x',opacity=0.5)

I sometimes do it using my own code.

x,theta=var('x,theta')
def Vol_Rx(f,x,theta,k):
    return([x,-sin(theta)*(f(x)-k),cos(theta)*(f(x)-k)+k])
def Vol_Ry(f,x,theta,k):
    return([(x-k)*cos(theta)+k,sin(theta)*(x-k),f(x)])
f(x)=sqrt(x)
a=0
b=3
p=parametric_plot3d(Vol_Rx(f,x,theta,0),(x,a,b),(theta,0,2*pi))
p+=parametric_plot3d(Vol_Rx(f,x,0,0),(x,a,b),color='red',thickness=3)
show(p)