Some school students, having begun to study stereometry, confuse volume and flat figures. So, for example, the sphere is called sometimes a circle, a cube – a square, and a rectangular parallelepiped – simply a rectangle. Respectively, such pupils quite often try to calculate the volume of a rectangle or the area of a cube.
It is required to you
- - ruler;
- - calculator.
Instruction
1. If the school student tries to calculate rectangle volume, then specify: about what specifically to a figure it is – a rectangle or its volume analog, a rectangular parallelepiped. Learn also: what is required to be found under the terms of a task – the volume, the area or length. Besides, find out: what part of the considered figure means – all figure, a side, an edge, top, the party or section the plane.
2. To calculate the volume of a rectangular parallelepiped, multiply among themselves its length, width and height (thickness). That is use a formula: V = a * b * c, where: a, b and with – length, width and height of a parallelepiped (respectively), and V – its volume. Previously lead all lengths of the parties to one unit of measure then the volume of a parallelepiped will turn out in the corresponding "cubic" units.
3. Example. What will be the tank capacity for water having the sizes: length – 2 meters; width – 1 meter 50 centimeters; height – 200 centimeters. Decision: 1. We lead lengths of the parties to meters: 2; 1.5; 2.2. We multiply the received numbers: 2 * 1.5 * 2 = 6 (cubic meters).
4. If the speech in a task goes after all about a rectangle, then for certain it is required to calculate its area. For this purpose just increase rectangle length by its width. That is apply a formula: S = a * b, where: an and b – lengths of the parties of a rectangle, S – the area of a rectangle. Use the same formula if in a task the side of a rectangular parallelepiped is considered – according to definition, it also has the rectangle form.
5. Example. The volume of a cube is 27 m³. What is the area of the rectangle formed by a cube side equal to? Decision. The cube edge length (which is as well a rectangular parallelepiped) equals to a root cubic of its volume, i.e. 3 m. Therefore, the area of its side (which is a square) will be equal to 3 * 3 = 9 m².