You will need

- - the range;
- calculator.

Instruction

1

If the student is trying to calculate the volume of a rectangle, specify: what kind of specific figure in question – the rectangle or its volumetric equivalent, rectangular parallelepiped. Find out: what is required to find the conditions of the problem – the volume, area or length. In addition, find out what part of the figure is a view of the whole figure, face, edge, vertex, face or cross-section plane.

2

To calculate the volume of a rectangular container, multiply between its length, width and height (thickness). That is, use the formula:

V = a * b * c,

where: a, b and C are its length, width and height of the box (respectively), and V is its volume.

All their sides are pre-reduced to one unit, then the volume of the parallelepiped obtained in relevant "cubic" units.

V = a * b * c,

where: a, b and C are its length, width and height of the box (respectively), and V is its volume.

All their sides are pre-reduced to one unit, then the volume of the parallelepiped obtained in relevant "cubic" units.

3

Example.

What will be the capacity of the water tank having dimensions:

length – 2 meters;

width – 1 meter 50 centimeters;

height – 200 cm.

Solution:

1. Given the lengths of the sides to meters: 2; 1,5; 2.

2. Multiply the resulting numbers: 2 * 1,5 * 2 = 6 (cubic meters).

What will be the capacity of the water tank having dimensions:

length – 2 meters;

width – 1 meter 50 centimeters;

height – 200 cm.

Solution:

1. Given the lengths of the sides to meters: 2; 1,5; 2.

2. Multiply the resulting numbers: 2 * 1,5 * 2 = 6 (cubic meters).

4

If we are in the task is still on the rectangle, you probably want to calculate its area. To do this, simply multiply the length of the rectangle by its width. That is, apply the formula:

S = a * b,

where:

a and b are the lengths of the sides of the rectangle

S – the area of a rectangle.

Use this same formula if the problem is considered a face of a rectangular parallelepiped according to the definition, it also has the shape of a rectangle.

S = a * b,

where:

a and b are the lengths of the sides of the rectangle

S – the area of a rectangle.

Use this same formula if the problem is considered a face of a rectangular parallelepiped according to the definition, it also has the shape of a rectangle.

5

Example.

The volume of a cube is 27 m3. What is the area of the rectangle formed by the face of the cube?

Solution.

The edge length of the cube (which is also a rectangular parallelepiped) is equal to the cubic root of its volume, i.e. 3 m. Therefore, the area of one side (a square) is equal to 3 * 3 = 9 m2.

The volume of a cube is 27 m3. What is the area of the rectangle formed by the face of the cube?

Solution.

The edge length of the cube (which is also a rectangular parallelepiped) is equal to the cubic root of its volume, i.e. 3 m. Therefore, the area of one side (a square) is equal to 3 * 3 = 9 m2.

# Advice 2: How to calculate the volume

The volume is the space occupied by the body. To calculate the correct volume of the object, which can easily determine the parameters (length, width, height) easy. It is only necessary to multiply the found value. To determine the volume of arbitrary shapes is much more difficult.

Instruction

1

A method of measuring the volume of the object with water was open to the Greek scientist Archimedes. To determine the volume of any body need to take a container of liquid, it is better if the container is transparent. The vessel must be applied to the scale division and to measure the volume occupied by water. After that, the water should immerse the body whose volume you want to learn. As soon as the water rises, you must mark the new level. The difference in levels, obtained by measurement and is equal to the volume of the immersed body.

2

In addition, it is possible to determine the volume of the object by measuring the amount of water displaced by it. For this purpose, in a vessel brim full of water, it is necessary to load the body. With the displaced water should be poured into another container and measure the volume, which will be equal to the desired volume of the body.

3

When finding the volume of a hollow body you can also use the water. For this you need to fill it are available, subject, and then pour the water into a glass, which is applied to the scale division. The measured body volume is equal to the volume of contained water in it.

4

You can calculate the volume of any body, knowing its density and mass. It is necessary to divide the available mass of the object on its density. To know the density of the material from which made a particular item from the reference table "Density of solids".

5

To calculate some of the figures are derived mathematical formulas. For example, for finding the volume of a cylinder we need to know its radius and height. The volume of a cylinder you will receive by works of "PI" to the square of the radius and height of the body (V=π*R2*H).

# Advice 3: How to calculate the area of a cube

The cube is a special case of a parallelepiped, in which each of the faces formed by the right polygon is a square. Only the cube has six faces. To calculate the area is not difficult.

Instruction

1

Initially, you need to calculate the area of any squares, which is a face of this cube. The area of a square can be calculated by multiplying at each other a couple of its sides. The formula can be expressed as:

S = a*a = a2

S = a*a = a2

2

Now that we know the area of one of the edges of the square, you can see the area of the whole surface of the cube. This can be done by modifying the formula listed above:

S = 6*a2

In other words, knowing that such squares (faces) of the cube have as many as six pieces, the surface area of the cube is one of the areas of the faces of the cube.

S = 6*a2

In other words, knowing that such squares (faces) of the cube have as many as six pieces, the surface area of the cube is one of the areas of the faces of the cube.

3

For clarity and convenience, you can give an example:

For example, given a cube whose edge length is 6 cm, it is required to find the surface area of this cube. Initially you will need to find the area of the face:

S = 6*6 = 36 cm2

Thus, knowing the area of the face, you can find the entire surface area of a cube:

S = 36*6 = 216 cm2

Answer: the surface area of a cube with an edge equal to 6 cm is 216 cm2

For example, given a cube whose edge length is 6 cm, it is required to find the surface area of this cube. Initially you will need to find the area of the face:

S = 6*6 = 36 cm2

Thus, knowing the area of the face, you can find the entire surface area of a cube:

S = 36*6 = 216 cm2

Answer: the surface area of a cube with an edge equal to 6 cm is 216 cm2

Note

The cube is a special case not only of a parallelepiped, and prisms.

A parallelepiped is the prism whose base is a parallelogram. Feature of box is that 4 of its 6 sides - rectangles.

Prism is the polyhedron whose base are equal polygons. One of the main features of the prism can be called that the side faces is a parallelogram.

In addition to Cuba, there are other types of polyhedra: pyramids, prisms, parallelepipeds, etc., each of which correspond to different ways of finding the areas of their surfaces.

A parallelepiped is the prism whose base is a parallelogram. Feature of box is that 4 of its 6 sides - rectangles.

Prism is the polyhedron whose base are equal polygons. One of the main features of the prism can be called that the side faces is a parallelogram.

In addition to Cuba, there are other types of polyhedra: pyramids, prisms, parallelepipeds, etc., each of which correspond to different ways of finding the areas of their surfaces.

Useful advice

If not given cube, and another is a right polyhedron, in any case, the surface area will be similar. This means that the surface area of regular polyhedron is found by adding together all the areas of its faces regular polygons.

# Advice 4: How to calculate the volume of the parallelepiped

A parallelepiped is a prism (polyhedron), the base of which lies the parallelogram. Have a

**cuboid**- has six faces, also parallelograms. There are several types**of the box**: rectangular, straight, slanted and cubic.Instruction

1

Direct is called a parallelepiped, whose four lateral faces rectangles. To calculate the volume we need the area of the base times the height V=Sh. Suppose the base

**of a parallelepiped**is a parallelogram. Then the footprint will be equal to the product of its side on height spent to this side - S=AC. Then V=ach.2

Called straight rectangular parallelepiped in which all six faces - rectangles. Examples: a brick, a matchbox. To calculate the volume we need the area of the base times the height V=Sh. The footprint in this case is the area of a rectangle is the product of the magnitudes of two of its sides S=ab, where a is width, b - length. So, obtain the required volume V=abh.

3

Sloping is called a parallelepiped, the side faces which are not perpendicular to the faces of the base. In this case, the volume equals the area of the base to a height - V=Sh. The height of the slanted

**parallelepiped**perpendicular segment dropped from any of the top vertex on the corresponding side of base side faces (that is, the height of any lateral face).4

A cube is called a direct box, which has all edges equal and all six faces are squares. The volume equals the area of the base to a height - V=Sh. Base - square, the base area of which is equal to the product of its two sides, i.e., the value side of the square. The height of the cube - the same size so the volume will be the size of the cube erected in the third degree is V=a3.

Note

The base of the box are always parallel to each other, it follows from the definition of the prism.

Useful advice

Dimension of the parallelepiped is the length of its edges.

Volume is always equal to the product of the square base to the height of the parallelepiped.

The volume of the slanted parallelepiped can be calculated as the product of the magnitude of the lateral edges of the square perpendicular cross-section.

Volume is always equal to the product of the square base to the height of the parallelepiped.

The volume of the slanted parallelepiped can be calculated as the product of the magnitude of the lateral edges of the square perpendicular cross-section.