 In practice problem 2, we're asked to find the radius of the base of a cylinder if the surface area is 528 pi square feet and the height is 10 feet. If you don't know where to start on these kind of problems, shall we start with the formula? We're asked if we're talking about the surface area of a cylinder? So I'm going to start this off by writing out the formula for the surface area of a cylinder and go from there. The surface area of a cylinder is 2 pi r squared plus 2 pi r h. And then let's look at what information is given to us. We're asked to find the radius. So I'm going to circle the r's because that's what we're going to solve for. And then we're given some pieces of information. We're given that the total surface area is 528 pi. So we're going to plug that in for the total surface area. And we're also given that the height is 10. And that's over here the height being 10. And then we're just going to fill in the rest of the formula and see what we have. So the total surface area 528 pi equals, we're going to leave it in pi form 2 pi r squared plus 2 pi r times h. And I'm going to go ahead and simplify this. I have three separate terms. 528 pi cannot be simplified anymore because we're going to leave it in pi form. 2 pi r h is simplified. But I have 2 times pi times r times 10. So I'm going to combine the 2 times 10 equals 20 pi times r. So now I have this equation and the only missing values are r. And that's what I'm trying to find, the radius of the base of the cylinder. And I'm going to simplify this even more. If you see each of these three terms has pi in it. So I can divide by pi and get rid of the pi to simplify this. And you'll also notice that each of these numbers is even. So I'm going to simplify that further by dividing out a 2. They're all divisible by 2. So I can clean up this equation. If I divide everything by the same thing, 2 pi, you'll see what happens here. The pi's are going to cancel in each of these terms. And then I'm going to clean up the rest of it. 528 divided by 2, you get your calculators out, is 264. 2 divided by 2, those are going to cancel out and all I'm left with in this term is r squared. And then 20 divided by 2 of course is 10. And I have the r there as well, 10r. Now that I've cleaned that up, it looks a lot easier to solve. And you should notice that this is a quadratic equation because I have a squared term r squared plus 10r. And then the constant number 264. If you see an equation that has a squared term in it, that should be a clue that you're going to factor this and we're going to put it in standard form and see what we have. To put it in standard form, I just have to move that 264 over, set everything equal to 0, and I'm going to have r squared plus 10r minus 264 equals 0. And now I can go ahead and factor this. This one's a little tricky because 264 is a pretty big number. We have to find the factor pairs of 264 that will add or subtract to 10. Why don't you pause the video and see if you can play around with some numbers and come up with the factor pairs that will work for this equation. And the numbers that work for this, the factor pairs of 264 are 22 and 12. That may have taken a while to get, but if you play around enough you'll get that because the difference 22 and 12, 22 times 12 equals 264. And then to get this positive 10, I would have a positive 22 and a negative 12. So when I factor that out, it's going to be r plus 22, r minus 12 equals 0. And to solve that then, my final answer r equals negative 22 or positive 12. And then the final step is to realize that what we're asked to find is the radius of the base of the cylinder. We can't have a negative distance, so we can't have a negative radius. And so my final answer is just going to be r equals 12. The radius of the base of my circle is 12.