WOLFRAM|DEMONSTRATIONS PROJECT

Strips of Equal Width on a Sphere Have Equal Surface Areas

​
strip 1 position
-1
strip 2 position
1
thickness
0.5
surface area =
b
∫
a
2πy
1+
2
dy
dx
x
strip 1
strip 2
a
1
=
-1
a
2
=
1
b
1
=
-0.500
b
2
=
1.500
surface area
=
12.5664
surface area
=
12.5664
On a sphere, strips of equal width have equal surface areas. The sphere is generated by revolving the semicircle given by
y=
16-
2
x
about the
x
axis.