Advice 1: How to make a scan of the cylinder

The cylinder is one of the basic three-dimensional figures. The cylinders are elliptic, circular and parabolic. The form of the cylinder is determined by which flat figure lies at its base. The most common (and simple to construct) case is a straight circular cylinder.
How to make a scan of the cylinder
You will need
  • paper;
  • pencil;
  • - the range;
  • a pair of compasses.
Direct circular cylinder is defined by two quantities: the base radius R and height of the cylinder H. Knowing the radius of the circle lying at the base of the cylinder, it is easy to compute the circumference of the base. This value is necessary to build a scanner. It is equal to L = 2NR, where Π=3,14159.
Any cylinder has two bases and the lateral surface. In a right circular cylinder both bases are circles. Side surface while unrolling it onto the plane looks like a rectangle with sides L (length of the circumference of the base) and H (height of cylinder). Thus, the scan of a right circular cylinder contains a rectangle and two circles.
Construct with compass two of the same circle of radius R. Then use the ruler and pencil, draw a rectangle with length H and height L = 2NR. Provide fields for the bonding of the figure. It is convenient to make a long strip for gluing on one side H of the rectangle and a small triangular field on both sides of the L. the Total sweep look at the picture.
If the cylinder is elliptic, the base it is an ellipse. Then in the above algorithm instead of circles draw ellipses, and the length L1 of the ellipse calculated according to the following table. The rectangle (the lateral surface) in this case dimensions H x L1.

In the case of the truncated at an angle to the base of the cylinder will have to build the surface of the cross section in true size.

Advice 2 : How to find the volume of a cylinder

Cylinder refers to three-dimensional geometric shapes, the so-called solids of revolution. Its bases are equal circles. The cylinder can be straight and inclined.
How to find the volume of a cylinder
You will need
  • — the range;
  • calculator.
In that case, if you know the area of at least one of the bases of the cylinder (they are equal), measure its height. To do this, drop a perpendicular from one base cylinder on to another, and measure its length. The height of the straight cylinder is equal to any of the sides. Then find the volume by multiplying the area of one of the bases of the cylinder S to the height h (V=S∙h). For example, if you know that the area of the circle lying at the base of the cylinder is 8 cm2 and its height is 5 cm, then its volume is V=8∙5=40 cm3.
In that case, if the base area of the cylinder is unknown, its volume can be found using another formula. Measure the height of the cylinder in any convenient way. Then, find the diameter of the base of the cylinderby measuring its convenient way, for example, using a ruler or calipers. Calculate the radius of the cylinderby dividing the diameter by 2. Find the volume of this geometric body by multiplying the number π≈3,14 the square of the radius R and the height of the cylinder h (V= π∙R2∙h).
Example.Find the volume of a cylinder, whose base has a diameter of 6 cm and the height is 5 cm Determine the base radius of the cylinder R=6/2=3 cm Calculate the volume V= 3,14∙32∙5=141,3 cm3.
If the cylinder is inclined, the above formula remains valid, but the height in this case is not equal to the generatrix. Therefore, in order to find the volume, measure the length of the generatrix l, and multiply it by the area of the base S, which can be found as described above, and the sine of the angle α between the generatrix and the plane of the base V=S∙l∙sin(α).
Example. Forming a circular cylinder has a length of 16 cm and is at an angle of 45 ° to the base. Find the volume of a cylinderif the base radius is 8 cm First, find the area of the base of the cylinder. It is equal to S=π∙R2. Substitute the value of this formula in the expression for the volume and get V= π∙R2∙l∙sin(α)=3,14∙82∙16∙sin(45°)≈2273,6 cm3.
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