Welcome to Geometry for beginners. Despite the fact that the title refers to "newcomers", topics relating to three-dimensional shapes, really come from the last part of a typical course of geometry. Congratulations! You have learned a lot, including all the necessary polygon formulas from your earlier work with two-dimensional shapes; therefore, dealing with spheres, prisms, cylinders, cones, etc., will not be as difficult as you might think. This article covers the cylinder.
The cylinder is a very often used form. Students, if you drink a can of pop music now, you hold a top hat. Canned goods in your pantry are cylinders. Cylinders can be short, like canned tuna, or tall and narrow, like Pringles chips.
Cylinders look like prisms because they have two bases — upper and lower, and they can be inclined or right. This means that the formulas for surface area and cylinder volume will have the same format as for prisms. However, prisms have polygons for the bases, so there are many side faces. On the other hand, the cylinders have circles for the bases, so there is only one side surface.
As with all three-dimensional shapes, the most common use of the surface is packaging or material - metal or cardboard - necessary for the manufacture of a cylinder. Sometimes there is a separate label that does not include the top and bottom. Consider a label on a can of tuna. If you make a vertical cut on the label and clear the label, you will find that it is just a rectangle whose height is the height of the can and its width is the circumference of the circular base.
Since cylinders and prisms are so similar, we can initially use the same formula for surface area.
The formula for the surface area of the cylinders: SA = 2B + LAwhere SA refers to surface area, B refers to AREA base, and LA refers to the side area,
I urge you to remember this formula, and not try to remember the next version. As long as you know the formulas for the circle and the area of the circle, you can continue to work with the original replacement formula without taking anything else. Do not forget to say the formula in words and replace what you say in the formula.
"The surface area of the cylinder is equal to twice the base area plus the lateral area of the cylinder." Since the base is a circle and the side surface is a rectangle, the formula changes to SA = 2 (pi r ^ 2) + (2 pi r) h. Note. Do not bother to remember this form of the formula. To restore it, it takes only a few seconds. The same is true for volume formulas.
The formula for the cylinder volume: A = B hwhere A - area, B - AREA base and h is the height of the cylinder, Memorize this formula, and then replace the corresponding circle formula. As a result, we obtain A = (pi r ^ 2) h.
A few things to remember:
1. Surface area should be labeled as square units.
2. Volume should be labeled as cubic units.
3. The final answer form can be left with pi, which is accurate, or you will use the pi key on your calculator for the decimal approximation. For real-life applications, we want a decimal answer. Ask your teacher about the rounding of the decimal point and don't forget the label.
