# How to find the volume of the knowledge area

The volume of geometric shapes - one of its parameters, quantitatively characterizing the space that this figure occupies. In three-dimensional figures, there is another option - the surface area. These two parameters are linked by certain ratios, which allows, in particular? calculate the amount of correct figures, knowing their surface area.

## Instruction how to find the volume of the knowledge area

Step 1:

The surface area of the sphere (S) can be expressed as the product of the number Pi quadruple in the squared radius (R): S = 4 * π * R². The volume (V) of the ball, this limited scope, can also be expressed in terms of range - it is directly proportional to the product of four times the number Pi to the radius cubed, and inversely proportional to the troika: V = 4 * π * R³ / 3. Use these two expressions to obtain a formula for calculating the amount by linking them through the range - expressing the radius of the first equation (R = ½ * √ (S / π)) and substitute it in the second identity: V = 4 * π * (½ * √ (S / π)) ³ / 3 = ⅙ * π * (√ (S / π)) ³.

Step 2:

A similar pair of expressions you can make up for the surface area (S) and volume (V) of the cube, linking them through the edge length (a) of this polyhedron. The volume of the third degree is equal edge length (√ = a³), and surface area - increased by six times the second level of the same shape parameter (V = 6 * a²). Express edge length through the surface area (a = ³√V) and substitute in the formula for calculating the volume of: V = 6 * (³√V) ².

Step 3:

Sphere volume (V) can be calculated by the total surface area is not, as a separate segment (s), whose height (h) is also known. The area of the surface area must be equal to the product of twice the number Pi to the radius of the sphere (R) and the height of segment: s = 2 * π * R * h. Get from this equation the radius (R = s / (2 * π * h)) and to substitute a formula relating the volume with a radius (V = 4 * π * R³ / 3). As a result of simplifying the formula, you should have an expression: V = 4 * π * (s / (2 * π * h)) ³ / 3 = 4 * π * s³ / (8 * π³ * h³) / 3 = s³ / (6 * π² * h³).

Step 4:

To calculate the volume of a cube (V) on one of its faces the area (s) any additional parameters needed to know. The length of the rib (a) the right hexahedron can find the square root of the face area (a = √s). Substitute this expression into the formula relating to the size of the volume of the cube edges (V = a³): V = (√s) ³.