Did you know that if you cut a spherical loaf of bread into slices of equal width, each slice will have the same amount of crust To see why, suppose the semicircle y r 2 x 2 shown here is revolved about the x axis to generate a sphere Let AB be an arc of the semicircle that lies above an interval o...

To show that the area swept out by arc AB does not depend on the location of the interval we need to ...

Did you know that if you cut a spherical loaf of bread into slices of equal width,

Question:

Did you know that if you cut a spherical loaf of bread into slices of equal width, each slice will have the same amount of crust? To see why, suppose the semicircle y = √r² - x² shown here is revolved about the x-axis to generate a sphere. Let AB be an arc of the semicircle that lies above an interval of length h on the x-axis. Show that the area swept out by AB does not depend on the location of the interval.