Geometry Problem: Show Area & Volume of Sphere & Cylinder

[ber8]

Guys please help me with this:

1) Show that the slice z=c of the sphere x² + y² + z² =1 has the same area as the slice z=c of the cylinder x² + y² =1 outside the cone x² + y² = z².

2) Deduce from the previous problem, and the known volume of the cone, that the volume of the sphere is 2/3 the volume of the circumscribing cylinder

Thanks in advance

 

[Unrest]

Guys please help me with this:

1) Show that the slice z=c of the sphere x² + y² + z² =1 has the same area as the slice z=c of the cylinder x² + y² =1 outside the cone x² + y² = z².

Calculate the areas of those two shapes, then show that their equations are equal. To find the area between the cone and cylinder, find them both and subtract.