Cross section is formed at right angle in relation to a longitudinal axis. And, the section of different geometrical figures can be presented by various forms. For example, at a parallelogram the section on appearance reminds a rectangle or a square, at a cylinder – a rectangle or a circle, etc.
It is required to you
- - calculator;
- - basic data.
Instruction
1. To find parallelogram cross-sectional area, it is necessary to know value of its basis and height. If, for example, only length and width of the basis is known, then find diagonal, using for this purpose Pythagorean theorem (the hypotenuse length square is equal in a rectangular triangle to the sum of squares of legs: a2 + b2 = c2). So, c = sqrt (a2 + b2).
2. Having found value of diagonal, substitute it in formula S = to c*h where h is parallelogram height. The received result will also be size parallelogram cross-sectional area.
3. If section passes along two bases, then calculate its area by a formula: S=a*b.
4. For calculation of the area of axial section of a cylinder passing perpendicular to the bases (provided that one party of this rectangle is equal to basis radius, and the second – cylinder height), use formula S =2R*h in which R – the size of radius of a circle (basis), S – cross-sectional area, and h – cylinder height.
5. If under the terms of a task the section does not pass through an axis of rotation of a cylinder, but at the same time parallel to its bases, so the party of a rectangle will not be equal to diameter of a circle of the basis.
6. Independently calculate the unknown party by creation of a circle of the basis of a cylinder, carrying out perpendiculars from the party of a rectangle (section plane) to a circle and calculation of the size of a chord (on Pythagorean theorem). After that substitute in S =2a*h the received value (2a – value of a chord) and calculate cross-sectional area.
7. The cross-sectional area of a sphere is determined by formula S = πR2. Pay attention that if the distance from the center of a geometrical figure to the plane coincides with the plane, then cross-sectional area will be equal to zero because the sphere concerns the plane only in one point.