The simplest cylinder is the figure formed at rotation of a rectangle around one of its parties. Such cylinder is called direct circular. Cylinders meet everywhere in science and technology and also as a part of difficult solids. Sometimes before the person there can be a task is to find cylinder surface area.
Instruction
1. The surface area of a cylinder consists of the area of its side surface and also the areas of the bases of a cylinder. At a simple circular cylinder of the basis represent circles of the set radius R. Square of one such circle it is equal πR². The bases are equal among themselves therefore this area should be considered twice.
2. If to develop a side surface of a direct circular cylinder on the plane, then the rectangle will turn out. One of the parties of this rectangle is equal to H cylinder height, and another - length of a circle of the basis of a cylinder or 2πR. Thus, the area of this rectangle, so and side surface of a cylinder, is equal 2πRH.
3. Now it was necessary to summarize the found areas of two bases and the area of a side surface: πR² + πR² + 2πRH = 2πR (R + H).
4. For example, there is a cylinder 10 cm high and with a radius of basis of 5 cm. Transfer units to the SI system if it is required: 10 cm = 0.1 m, 5 cm = 0.05 m. Now calculate the areas of the basis and a side surface. Area of the basis of such cylinder of Sa = 3.14*0.05² m² = 0.00785 m². Area of a side surface of this cylinder of Sb = 2*3.14*0.05*0.1 m² = 0.0314 m². Area of all surface of a cylinder 2Sa + Sb = 2*0.00785 m² + 0.0314 m² = 0.0471 m².