 Cylinders 
At the left is a cylinder. This isn't really a prism, since the side that wraps around isn't really flat, but everything works the same as if it were one. Notice that the top and bottom are identical, and they're circles. In order to calculate the surface area of a cylinder, you will need to be able to find the area of a circle. The radius of each circle is 4 cm. (You might want to review PI and the circle area formula first). The cylinder has three faces ... the top and bottom circles, and the flat part that wraps around them, which would be a rectangle if you were to open it up. 
That's just what we did, in the picture at the left. You can see clearly that the two ends of the cylinder are both circles. We'll need the radius of each in order to find the area, and we know that. The piece that wraps around them is obviously a rectangle. We'll need to know its length and width in order to calculate its area. The width is clearly 10 cm, ... but what is its length? The length of this rectangle represents the distance that wraps around the circular ends. But you know this distance ... it's the circumference of a circle! We may not know the actual length, but we know it's the circumference of a circle, and we have a formula for that:  We can use this for the length of the rectangle. Let's calculate the total surface area: 
Top circle:  Bottom circle: Rectangle:  The total surface area is 50.27 + 50.27 + 251.33 = 351.9 cm2 There is a formula for the surface area of a cylinder:  ... where r is the radius of the cylinder and H is the height of the cylinder. You can calculate the surface area in one step on a calculator. Once again, here's an explanation of where the formula comes from:  (The area of two circles and a rectangle, where length and width of the rectangle are the circumference and height of the cylinder). Again, make sure your teacher will allow you to use this formula for your work; in grade 7/8 classes you may be asked to calculate surface area step-by-step instead, like we did at the top of the page. |