>

 

>	with(plots):  # make sure you load this package first

 

Place your cursor in each frame. Click and rotate. 

#69 in 6.2    Circular hole within a cylinder 

>	bigcylinder:= plot3d( sqrt(16 - x^2), x=0..4, y=-5..5, grid=[40,40], axes=normal, scaling=constrained,  color=yellow, title=` horizontal cylinder - radius 4 `):

 

>	bigcylinder;

 

>	vert_hole:= cylinderplot(2, phi=-Pi/2..Pi/2, z= 0..4, scaling=constrained, color=green, axes= normal, style=patch, grid=[45,45]):  # hole of radius 2

 

>	vert_hole;  display({vert_hole, bigcylinder}, title = ` upper hole within a cylinder `);

 

From this picture, set up a narrow strip parallel to the x-axis. The top of the strip is part of the cylindrical surface. The method here is the same as one shown in Example 7. 

#70  A hole within a sphere 

>	quar_sph4:= sphereplot(4, phi=-Pi/2..Pi/2, theta = 0..Pi/2, grid= [40,40], scaling=constrained, axes=normal, color= yellow, title = ` quarter_sphere of radius 4 `): quar_sph4;

 

>	display({hemi_sph4, vert_hole}, axes=boxed);

 

This problem can be done either by strip or by rotation.