Before finding the height of a truncated cone , read its definition. A truncated cone is called a figure which is formed by a perpendicular cross-section plane of an ordinary cone, provided that the cross section parallel to its base. This figure has three characteristics:
- r1 - the largest radius;
- r2 is the smallest radius;
- h is the height.In addition, as a conventional cone, truncated there is a so-called forming, denoted by the letter l. Note the inner section of the cone: it is an isosceles trapezoid. If it is rotated around its axis, you get a truncated cone with the same parameters. In this case, the line that divides the isosceles trapezoid into two smaller ones, coincides with the axis of symmetry and height of the cone. The other side is the generatrix of the cone.
Knowing the radii of the cone and its height, you can find its volume. It is calculated as follows:V=1/3πh(r1^2+r1*r2+r2^2)If we know the two radii of the coneand its volume, this is enough to find the height of the figure:h=3V/π(r1^2+r1*r2+r2^2).In that case, if the condition of the problem the diameters of the circles, not the radius, this expression takes on a slightly different form:h=12V/π(d1^2+d1*d2+d2^2).
Knowing the forming of the cone and the angle between it and the base of this shape, you can also find her height. To do this, from the other vertices of the trapezoid to hold the projection to a larger radius to form a smaller right triangle. The projection will be equal to the height of the truncated cone. If you know l and forming the angle, the height is determine by the following formula:h=l*sinα.
If the problem statement is known, only the cross-sectional area of the cone, find the height is impossible unless you know both its radius.