The question of how to find the volume of a cylinder may arise not only for a student who studies stereometry. Today, streamlined and smooth forms are very popular in architecture and interior design. The cylinder is one of them. By itself, it is a body of revolution - a rectangle that has been rotated 360 degrees around one of the sides. Columns, pistons, pots, cups, glasses, vases, etc. have this shape. Of course, information about finding the volume of a cylinder can rarely be useful in everyday life, but at school they devote a lot of time to this topic, so you should not ignore it.
Standard way to determine the volume of a cylinder
In order to understand the features of the volume of a cylinder, we need to return to the topic of a parallelepiped. This body has a base in the form of a rectangle or square. To calculate the volume of such a geometric figure, you need to multiply the area of \u200b\u200bthe base (S \u003d a × b) by the height. With a cylinder, everything is by analogy. The basis is a circle, the area formula of which is S=πR2. Height is any vertical line,most often choose the one that connects the centers of the bases.
How to find the volume of a cylinder along the diagonal section?
Sometimes it may happen that in the conditions there will be no necessary values, then it will be necessary to find them from the drawing, using the properties of the cylinder. The most frequent example of such a case are problems in which the diagonal of the section is known and one of the components of the volume formula is the radius or height. A task with a similar condition can be considered typical for this topic. There is only one thing to remember for the solution: the height of the cylinder is any vertical line that connects the bases and creates a 90 degree angle with them. Using this feature, you can easily determine that the diagonal of the section (which is a cube or rectangle), radius and height together create a triangle. Its sides can be found using the Pythagorean theorem.
