You will need
- textbook on geometry and mathematics.
So, in order to find the surface area of a cube, calculate the area of one face and multiply it on the total number, that is, use the formula: SN=6*x*x=6*x^2 where x is the edge length of the cube.Example. Let the edge length of the cube is 4 cm, then total surface area is equal to SN=6*4*4=6*4^2=96 cm^2.
In order to calculate the volume of a cube, you need to find the area of the base and multiply it by the height, edge length). And since the cube has all faces and edges are equal, then we obtain the following formula: V=x*x*x=x^3.Example. Let the edge length of a cube is 8 cm, then the volume V=8*8*8=512 cm^3.In mathematics there is such a thing as curly. Out of it came the expression "to Erect a number in the cube (third power of that number).
The radius of the inscribed sphere is given by: r=(1/2)*x.Example. Let the volume of a cube is 125 cm^3, then the radius of the inscribed sphere is calculated in two stages. First, find the edge length for this calculate the cube root of 125. It will be 5 cm And then calculate the radius of the inscribed sphere r=(1/2)*5=2.5 cm by the Way, the sphere will touch the cube at exactly six points.
The radius of the sphere described by the following formula: R=((3^(1/2))/2)*x.Example. Let the radius of the inscribed sphere r equal to 2 cm, then in order to find the radius of the sphere is described, it is necessary, first, to find the length of its edges: x=r*2=2^2=4 cm, and the second, and the radius: R=((3^(1/2))/2)*4=2*3^(1/2) see the Cube will touch the sphere at eight points. These points are its vertices.
The length of the diagonal of a cube can be calculated by the formula: d=x*(3^(1/2)).Example. Let the edge length of the cube is 4 cm, then, using the above formula, we get: d=4*(3^(1/2)) see it is Worth Recalling that the diagonal of a cube is called a segment, which connects two symmetrically located peaks and passes through its center. By the way, in Cuba there are four.
Always observe the dimensions.
Advice 2: How to measure diagonal
For convenience, denote the size of the screen of TV or monitor use of the length of its diagonal - this allows you to specify the size of just one number. It so happened that the number is most often expressed in inches, are not used in most countries that have adopted the metric system of measurement. In Russia, too, the length is measured in inches, but the screen size is still expressed in inches.
If you, too, believe the school teacher, the diagonal of a rectangle is the length between the opposite corners, passing through the center of the figure. Measure this segment of a rectangular screen of your monitor or TV. The tool can serve as a centimeter, measuring ruler, meter, or other available tool, which can be used without fear to damage the surface of the tube or matrix.
And if the school you still remember the Pythagorean theorem, it is possible to do even trickier to measure is the diagonal length and width, and the desired value to compute the root from the sum of the squares of the resulting values. Sometimes using this method is preferable as it guarantees the safety of the surface of a CRT or matrix.
Obtained in the previous steps, the number must be in inches. Usually in these units is indicated by the size of the screen, so most likely, you need it in those units. Every inch contains approximately 2.54 cm, so divide by this value, measured in centimeters the length of the diagonal.
Measure is meaningful only in cases where simpler methods are unavailable. For example, almost always on the body of the device with the screen you can find marking in which one of the numbers indicates the size diagonally. For example, if the designated monitor SyncMaster 2232BW, the first two digits in the numerical designation refer to the diagonal size in inches. If it is necessary to know the diagonal in inches, perform a mathematical operation, the inverse applied in the previous step - 22, multiply by 2.54.
Diagonal of the monitor screen by the numbers in its name, you can define not even examining the case. If the computer is turned on and the operating system is configured correctly, the full name along with the numbers can be seen by going to the settings screen. In Windows 7 and Vista, simply click on the desktop, right-click and select "screen Resolution". The full name of the monitor can be found in the "Screen" of the window.