### Video Transcript

Find the surface area of a circular cylinder whose volume is 1256 centimeters cubed and whose height is 16 centimeters. Use π is equal to 3.14.

With these type of questions, what I like to do first is to write down the information Iβve been given. So first of all, Iβve got the volume, π£, is equal to 1256 centimeters cubed. Then, I know the β, the height, is 16 centimeters. And weβre told to use π is equal to 3.14. So, the next thing I do is draw a sketch to help me visualize whatβs going on. So here, Iβve shown our cylinder. And Iβve got the height and also got the radius on there cause we donβt know the radius. And then next, what we need to do is consider what formulae we might use to help us solve the problem.

The first one is the volume of a cylinder, and this is equal to ππ squared β. And then next, what we need to consider is the formula for surface area. And that is two ππβ plus two ππ squared. And we get that cause the two ππβ is the surface area of our curved surface. And then, the two ππ squared is the surface area of our two end points, which are both circles. And the area of a circle is ππ squared, and we have two of them.

So now, what weβre gonna do is find π. And we can do that using our volume formula. If we substitute in our values to that formula, we get 1256, cause thatβs our volume, is equal to 3.14, the value that weβre using for π, multiplied by π squared multiplied by 16. So next, if we multiply the 3.14 and 16, we get 50.24. So therefore, weβve got 1256 equals 50.24π squared. Then, if we divide through both sides by 50.24, we get 25 is equal to π squared. And then, if we take the square root of both sides, we get five is equal to π. And weβre only interested in the positive result because weβre looking at a length, because weβre looking at radius. So, we now know that the radius is equal to five.

So now, what we can do, because weβve got the radius, is move on and find the surface area cause thatβs what we need to find, because weβve got all the information we need. So now, what we do is to find the surface area, substitute in our values into two ππβ plus two ππ squared.

When we do that, we get two multiplied by 3.14, our value for π, multiplied by five, which is our radius, multiplied by 16 and then plus two multiplied by 3.14 multiplied by five squared. And when we calculate this, what we get is 502.4 plus 157, which gives us our final answer of 659.4. And this is centimeters squared because weβre looking at an area. So therefore, we can say that the surface area of a circular cylinder whose volume is 1256 centimeters cubed and whose height is 16 centimeters is 659.4 centimeters squared.