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Use the Second Theorem of Pappus described in Exercise 48 to find the surface area of the torus in Example 7.

$4 \pi^{2} r R$

Applications of Integration

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in this problem, Willie's, uh, shape the tourists. In example. Seven less enough. We have a circle all located somewhere on here. And let's set. We are forming the tourists. Barbara, tightening to circle around y axis 20 line that we're rotating at is located Captain are away from the center of the circle. Why send drop the circle? Because we know that four circle the central it is located at the centre. Now, if he rotate this around the y axis, we know that we will get a doughnut shaped object and that will be the tours. Now, you know that surface area off the shape is to apply times or less right this way and being ordered surface area is equal to, um, distance traveled by de Seine droid. That's why by the, um Berkley now for a given object, we know that the radius is located somewhere or century is located here, and that is our away from the, um, rotational axis. It means that this has troubled will then be to pine times Capital are right. So it well, for such a dez and it'll trouble all this distance and it will be two part times are. What is the Ark link? Guilty or, you know, object. This cylinder, it is justice or comforts of the cylinder. So that is too high. Times are and service areas multiplication of those two. So that is four plants grade kept to our lower case far.