# problem from class: solid bounded by:
# z=1-y^2
# z = 0
# z=4-2x
# x=4
restart: with(plots):
P11:= plot3d( 1-y^2, x=( (3+y^2)/2 )..(4), y=-1..1,
axes=framed, shading=ZGRAYSCALE, style=PATCH ):
N:= 10:
S11:= [ [4, -1, 0],
seq([ 4, -1+2*n/N, 1-(-1+2*n/N)^2],
n=0..N) ]:
ps11:= polygonplot3d(S11, shading=ZGRAYSCALE ):
S12:= [ [2, -1, 0],
seq([ 1/2*(3+ (-1+2*n/N)^2) , -1+2*n/N, 1-(-1+2*n/N)^2],
n=0..N) ]:
ps12:= polygonplot3d(S12, shading=ZGRAYSCALE ):
P21:= plot3d(1-y^2, x=( (3+y^2)/2 )..(4), y=(1)..(sqrt(5)),
axes=framed, shading=ZGRAYSCALE, style=PATCH ):
P22:= plot3d(1-y^2, x=( (3+y^2)/2 )..(4), y=(-sqrt(5))..(-1),
axes=framed, shading=ZGRAYSCALE, style=PATCH ):
S21:= [ [4,-1,0], [4,1,0], [2,1,0], [2,-1,0] ]:
ps21:= polygonplot3d(S21, shading=ZGRAYSCALE ):
S22:= [ [4,1,0],
seq( [4, 1+(sqrt(5)-1)*n/N, 1 - (1+(sqrt(5)-1)*n/N)^2 ],
n=0..N)
, [4, -sqrt(5), -4],
seq( [4, -sqrt(5)+(-1+sqrt(5))*n/N, 1-( -sqrt(5)+(-1+sqrt(5))*n/N)^2 ],
n=0..N)
]:
ps22:= polygonplot3d(S22, shading=ZGRAYSCALE ):
S23:= [ [2,1,0],
seq( [ (3+ (1+(sqrt(5)-1)*n/N)^2)/2,
1+(sqrt(5)-1)*n/N, 1 - (1+(sqrt(5)-1)*n/N)^2 ],
n=0..N)
, [4, -sqrt(5), -4],
seq( [( 3+ (-sqrt(5)+(-1+sqrt(5))*n/N)^2)/2,
-sqrt(5)+(-1+sqrt(5))*n/N, 1-( -sqrt(5)+(-1+sqrt(5))*n/N)^2 ],
n=0..N)
]:
ps23:= polygonplot3d(S23, shading=ZGRAYSCALE ):
orient:= [-60,55]:
display(P11, ps11, ps12,
view=[(.8)..(4.2), (-1.2)..(1.2), (-.2)..(1.2)],
orientation=orient, title="Volume 1" );
display(P21, P22, ps21, ps22, ps23,
view=[(.8)..(4.2), (-2.4)..(2.4), (-4.2)..(1.2)],
orientation=orient, title="Volume 2" );