 These next two problems deal with hemispheres, and all that a hemisphere is is half of a sphere. So for number three, if we're finding the volume of a hemisphere, because we're doing volume, we want to make sure that we use the volume formula, which is four-thirds pi r cubed. But because we are doing a hemisphere, we want to multiply that by a half. So what we're going to do is multiply the fractions one times four and two times three, that's four over six. But if you reduce four over six, it's two-thirds. So what we're really doing when we do the volume of a hemisphere is use the formula two-thirds pi r cubed. So now I can enter in the radius of two inches. Two to the third power is eight, so we have two-thirds pi times eight. And again, like in the last problem, if you think of eight as eight over one and you multiply the fractions, you get sixteen over three, which cannot be divided. So sixteen over three pi, and that would be cubic inches because we're doing volume. In number four, we're going to find the surface area of the hemisphere if the area of the great circle is thirty-six pi. A couple of things here to note. First of all, surface area of a sphere is four pi r squared. But because we want to do a hemisphere, we want to multiply that by a half or divide it by two. And so we actually are just going to do two pi r squared. The other thing, though, that you have to remember is that when you do surface area, you're talking about what it would take to cover this hemisphere with, let's say, fabric or wrapping paper. Well, if I do two pi r squared, that's going to take care of the top and all of the sides. But you're still going to have the bottom part that needs to be covered. So we're actually going to add the area of a circle so that we can also wrap the bottom of this hemisphere. So we're going to do two pi r squared plus the area of the circle, which would be technically the bottom of this hemisphere. So that's pi r squared. Okay, now the next issue is that we need to find the radius. Now remember that the great circle and a sphere have the same radius. So if I know that the area of the circle pi r squared has to equal 36 pi, then I can divide both sides by pi to get r squared equals 36 and figure out that r is 6. So now I can use that to figure out the total surface area. Oops, meant to put in a 6 there. 2 pi times 6 squared plus pi times 6 squared. We get 2 times 36, which is 72 pi plus 36 pi. And when you add those two together, you get 108 pi. And this one doesn't have units, so we'll just say square units. So the surface area of a hemisphere, you have to make sure that you do half of a sphere formula. But then you also have to add the circle because the circle is the base of that hemisphere. If you think of maybe like a snow globe, you'd have to cover the bottom of it. And that's where we add the pi r squared.