 In these last two problems, we're going to find surface area and volume for figures that are made up of more than one three-dimensional figure. So if you look at number five, you can see that it is a shape that's made up of a cylinder with a hemisphere on the top of it. Now, if we're being asked to find the total surface area, keep in mind that that's like if we wanted to wrap this with fabric or paper. Well, what that means is that when we find surface area, we're actually not going to find the, or we don't want to include this base because we wouldn't wrap that with wrapping paper. We would wrap the sides of the cylinder, we'd wrap the bottom of the cylinder, and then we'd wrap the top of the hemisphere. And so when we find the total surface area for this figure, what we're going to do is we're going to use surface area of a cylinder but with only one base. And then we're going to add that to the surface area of the hemisphere. Okay, so you have to think back to chapter 12 for surface area of a cylinder. And remember that originally, surface area of a cylinder with two bases is 2 pi r h plus 2 pi r squared. So what we're going to do is we're going to do 2 pi r h plus instead of 2 pi r squared, because we don't want to do both bases, we only want to do one base. We're only going to do pi r squared. So again, the surface area of a cylinder is normally 2 pi r h plus 2 pi r squared, but because we only want to do one base, we don't want to include that top, we're just going to do pi r squared. And then plus the surface area of a hemisphere, if you remember that a sphere is normally 4 pi r squared, but a hemisphere is half of that, we're going to add 2 pi r squared. So that's the formula that we're going to use. And now it's just a matter of entering in the information. So 2 times pi times the radius, which they tell us is 2 times the height, which is 5, plus pi times 2 squared, plus 2 times pi times 2 squared. Just make sure that you do the correct order of operations here. Make sure you evaluate both of your powers before you multiply. So 2 pi times 2 times 5, that's going to be 20 pi, and then 2 squared, so that's going to be 4 pi, and then 2 squared is 4 times 2 is going to be 8 pi. So now when we add all of those together, we get 32 pi, and that's going to be square inches. So the surface area for this figure would be 32 pi square inches. In this problem, we're finding volume, and we can see that this shape is made up of a cone, a cylinder, and a hemisphere. So to find the volume, we're going to take the volume of the cone plus the volume of the cylinder plus the volume of the hemisphere. And we're going to add those together to get the total volume. Alright, so volume of a cone, we want to think back to section 13.2. Volume of a cone is 1 third times the area of the base, which is pi r squared, times the height of the cone. Plus volume of a cylinder, which is from 13.1, is the area of the base, pi r squared, times the height of the cylinder. Plus the volume of a hemisphere. Well, remember that the volume of a sphere is 4 thirds pi r cubed. So because we're doing a hemisphere, we're just going to do half of that. So 2 thirds pi r cubed. Now that we have our formulas, it's just a matter of entering in the information. And you'll notice that in the picture, we have the height of the cylinder. We have the height of the cone and the diameter of the circle, which is 4. So the radius that we're going to use is 2. So 1 third times pi times 2 squared times the height of the cone, which is 4. Plus pi times 2 squared times the height of the cylinder, which is 10. Plus 2 thirds times pi times 2 to the third. And then we'll evaluate. So in this first set of parentheses, 2 squared is 4. Times 4 is 16. Times 1 third, I'm just going to leave it as 16 thirds pi. Plus 10 times 4. So that's 40 pi. Plus 2 to the third power is 8. Times 2 is 16. So 16 over 3 times pi. And then you can go ahead and just put this into your calculator and give the approximate answer. So 16 thirds times pi plus 40 times pi plus another 16 thirds times pi. Should give you about 159.2. And this is volume, so it'll be cubic centimeters.