Advice 1: How to find the volume, knowing the area

The volume of geometric shapes - one of its parameters that quantitatively characterize the space that the figure occupies. From volume figures there is another parameter - the surface area. These two measures are linked by certain relations, which allows, in particular? to calculate the volume of regular figures, knowing the area of their surface.
How to find the volume, knowing the area
Instruction
1
The surface area of the sphere (S) can be expressed as a quadruple product of the number PI of squared radius (R): S = 4*π*R2. The volume (V) of the ball bounded by this sphere can also be expressed using the radius - it is directly proportional to the product of four times the number PI times the radius cubed, and inversely proportional to the three: V = 4*π*R3/3. Use these two expressions to get a formula calculate the volume, linking them via the radius - Express the radius of the first equality (R = ½*√(S/π)) and substitute it in the second identity: V = 4*π*(½*√(S/π))3/3 = ⅙*π*(√(S/π))3.
2
A similar pair of expressions you can make for the surface area (S) and volume (V) of a cube, linking them via the edge length (a) of this polyhedron. The volume is equal to the third degree of length of the rib (√ = a3), and the surface area is increased six times in the second degree of the same parameter figures (V = 6*a2). Express the edge length using the surface area (a = 3√V) and substitute in the formula for calculating the volume V = 6*(3-V)2.
3
The volume of a sphere (V) can be calculated and the area is not the entire surface, but only the individual segment (s) whose height (h) is also known. The area of the surface must be equal to the product of twice the number PI times the sphere radius (R) and the height of the segment: s = 2*π*R*h. Find from this equation the radius (R = s/(2*π*h)) and substitute into the formula linking the volume with the radius (V = 4*π*R3/3). As a result of simplification of the formula you should have this expression: V = 4*π*(s/(2*π*h))3/3 = 4*π*s3/(8*π3*h3)/3 = s3/(6*π2*h3).
4
To calculate the volume of a cube (V) area of one face (s) any additional parameters do not need to know. The edge length (a), regular hexahedron it is possible to find the square root of the face area (a = √s). Substitute this expression into the formula linking the volume with the size of the cube (V = a3): V = (√s)3.

Advice 2: How to find the volume of a cube formula

When solving many mathematical and physical problems it is required to find the volume of a cube. Since the cube is perhaps the simplest stereometric figure, then the formula for calculating its volume very simple. The volume of a cube equals the cube (third-degree) the lengths of its edges. However, it is not always the edge length is preset. In such cases it is necessary to use other formulas for finding the volume of a cube.
How to find the volume of a cube formula
You will need
  • calculator.
Instruction
1
To find the volume of a cube if you know the length of its edges, use the following formula:
V = A3, where V is the volume of a cube and the length of his ribs.
Calculated according to this formula the volume of a cube will have the proper cubic unit of measurement. For example, if the edge length is specified in millimeters (mm), the volume of a cube is measured in cubic millimeters (mm3).
2
To calculate the volume of a cube according to the above formula, take a scientific calculator. Type on the keyboard of the calculator the numerical value of the length of the edges of the cube. Click on the calculator button exponentiation. Depending on the type of calculator, this button may have a different view. But usually it's a couple of characters such as "xy" or "ab", and the second is slightly smaller and located a little higher. After you find and click the exponentiation, press the number "3" and then "=". The numerical value of the volume of a cube will appear on the display of the calculator.
3
To calculate the volume of a cube in ordinary ("accounting") calculator, use a simplified entry of the formula:
V = a * a * a, where V is the volume of a cube and the length of his ribs.
Enter the numeric value of the length of the ribs. Then press the multiply "x". Again, type the length of the ribs. Again, hit "x". And finally, re-type the length of the ribs. Then click "=".
4
To calculate the volume of a cube on the computer, use Windows calculator. Run the Calculator (start - > Run -> type calc). Switch to the mode of carrying out engineering calculations ("View" -> "Engineering"). Type on the virtual keyboard of the calculator or on the computer keyboard is the edge length of the cube. Then just press the virtual button "x^3". All the result is ready. Click on the button "=" is not necessary.
5
If the edge length of the cube is unknown, and set any other of its characteristics, to calculate its volume (V) use the following formulas:
V = (d / √2)3, where d is the diagonal of the cube face,

V = (D / √3)3 where D is the diagonal of the cube.

V = 8 * r3, where r is the radius of the sphere inscribed in a cube.

V = (2R / √3)3, where R is the radius of the sphere circumscribed about the cube.
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