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Finding Surface AreaSlicing bread Did you know that if you
Chapter 6, Problem 28E(choose chapter or problem)
Slicing bread 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 \(y=\sqrt{r^{2}-x^{2}}\) 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 of length h on the x-axis. Show that the area swept out by AB does not depend on the location of the interval. (It does depend on the length of the interval.)
Questions & Answers
QUESTION:
Slicing bread 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 \(y=\sqrt{r^{2}-x^{2}}\) 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 of length h on the x-axis. Show that the area swept out by AB does not depend on the location of the interval. (It does depend on the length of the interval.)
Step 1 of 3
In this problem, we have to show that surface area will be independent of AB.