How To Find The Volume Of The Body | The Science

The Science

How to find the volume of the body

Each body has three major characteristics: weight, volume and area. If you know the weight and type of material from which it is made, the problem of calculating the volume is trivial. However, in a number of tasks and the mass density of the body is not given, and there are other values, which are based on them and you want to find the volume.

Instruction how to find the volume of the body

Step 1:

Imagine that the body has a certain mass m and density ρ. If you know these two parameters, then applying a formula, calculate the volume of the body as follows: V = m / ρ If given the density and mass of not, find the last, knowing the other parameters. For example, for a given power and acceleration of the specified use to find the mass of the following formula: m = F / a Accordingly, the scope of the body get the formula: V = F / aρ, where F - the force of the body, a - acceleration of the body.

Step 2:

Under the terms of some of the tasks are not supported by any density or mass or acceleration, or force, and given a cuboid with a height c, a width a and length b. The height of the box is both its edge. In such cases, refer to the fact that the volume of the figure is the product of the above three quantities: V = abc if given in cubic problem, then, since all its faces - squares calculate volume as follows: V = a ^ 3

Step 3:

If the problem is given a prism, its volume is equal to the product of the area of ​​the base to a height of:. V = Sosn * H When the base of the prism there is a regular polygon, such a prism is called a right. Write down the formula for regular prism whose base is n-gon: V = nr ^ 2 * tgα / 2 * H, where nr ^ 2 * tgα / 2 - footprint Since about each polygon can be described by a circle having a certain radius, then α - this is the angle between adjacent radii of the circle.

Step 4:

If the problem is given a pyramid with a base and height, use the following equation:. Vpir = 1 / 3Sosn * H, where Sosn.. - Footprint. In a regular pyramid, like the prism, there is a basis, in which all sides are equal. Accordingly, the scope of the pyramid will be: V = 1 / 3nr ^ 2 * tgα / 2 * H

Step 5:

The volume of the ball get in terms of its radius or diameter: V = 4 / 3πR ^ 2 = 1 / 6πD ^ 2 The second body of rotation - a cylinder - formed by the rotation of a rectangle about its axis. Its volume is determined as follows: V = πR ^ 2 * H, where πR ^ 2 - footprint. If you rotate the right-angled triangle around its axis, you get a cone next volume: V = 1 / 3πR ^ 2 * H