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    • Speech therapy portal / Disgraphia / How to find the volume of a complex shape. Geometry Calculator - calculation of geometric shapes. Volumetric geometric shapes

    How to find the volume of a complex shape. Geometry Calculator - calculation of geometric shapes. Volumetric geometric shapes

    How to find the volume of a complex shape. Geometry Calculator - calculation of geometric shapes. Volumetric geometric shapes

    Geometric shapes are closed sets of points on a plane or in space, which are limited by a finite number of lines. They can be linear (1D), flat (2D), or spatial (3D).

    Any body that has a form is an aggregate geometric shapes.

    Any figure can be described by a mathematical formula of varying degrees of complexity. From a simple mathematical expression to the sum of a series of mathematical expressions.

    The main mathematical parameters of geometric shapes are radii, lengths of sides or faces, and the angles between them.

    Below are the main geometric shapes most often used in applied calculations, formulas and links to calculation programs.

    Linear geometric shapes

    1. Point

    A point is a basic measurement object. The main and only mathematical characteristic of a point is its coordinate.

    2. Line

    A line is a finite-length thin feature that is a chain of connected points. The main mathematical characteristic of a line is its length.

    A ray is a thin spatial object of infinite length and representing a chain of points connected to each other. The main mathematical characteristics of a ray are its origin and direction.

    Flat geometric shapes

    1. Circle

    A circle is a locus of points on a plane, the distance from which to its center does not exceed a given number, called the radius of this circle. The main mathematical characteristic of a circle is its radius.

    2. Square

    A square is a quadrilateral in which all angles and all sides are equal. The main mathematical characteristic of a square is the length of its side.

    3. Rectangle

    A rectangle is a rectangle with all angles equal to 90 degrees (straight lines). The main mathematical characteristics of a rectangle are the lengths of its sides.

    4. Triangle

    A triangle is a geometric figure formed by three line segments that connect three points (vertices of a triangle) that do not lie on one straight line. The main mathematical characteristics of a triangle are side lengths and height.

    5. Trapezoid

    A trapezoid is a quadrilateral in which two sides are parallel and the other two sides are not parallel. The main mathematical characteristics of a trapezoid are side lengths and height.

    6. Parallelogram

    A parallelogram is a quadrilateral whose opposite sides are parallel. The main mathematical characteristics of a parallelogram are the lengths of its sides and the height.

    A rhombus is a quadrilateral with all sides, and the angles of its vertices are not equal to 90 degrees. The main mathematical characteristics of a rhombus are its side length and height.

    8. Ellipse

    An ellipse is a closed curve on a plane, which can be represented as an orthogonal projection of a section of a circle of a cylinder onto a plane. The main mathematical characteristics of a circle are the length of its semiaxes.

    Volumetric geometric shapes

    1. Ball

    A ball is a geometric body that is a collection of all points in space located at a given distance from its center. The main mathematical characteristic of a ball is its radius.

    A sphere is a shell of a geometric body, which is a collection of all points in space located at a given distance from its center. The main mathematical characteristic of a sphere is its radius.

    A cube is a geometric body that is a regular polyhedron, each face of which is a square. The main mathematical characteristic of a cube is the length of its edge.

    4. Parallelepiped

    A parallelepiped is a geometric body that is a polyhedron with six faces and each of them is a rectangle. The main mathematical characteristics of a parallelepiped are the lengths of its edges.

    5. Prism

    A prism is a polyhedron, two faces of which are equal polygons lying in parallel planes, and the other faces are parallelograms that have common sides with these polygons. The main mathematical characteristics of a prism are base area and height.

    A cone is a geometric figure obtained by combining all rays emanating from one vertex of a cone and passing through a flat surface. The main mathematical characteristics of a cone are base radius and height.

    7. Pyramid

    A pyramid is a polyhedron whose base is an arbitrary polygon, and the side faces are triangles with a common vertex. The main mathematical characteristics of a pyramid are base area and height.

    8. Cylinder

    A cylinder is a geometric shape bounded by a cylindrical surface and two parallel planes that intersect it. The main mathematical characteristics of a cylinder are base radius and height.

    You can quickly perform these simplest mathematical operations using our online programs... To do this, enter the initial value in the corresponding field and press the button.

    This page presents all the geometric shapes that are most often found in geometry to represent an object or part of it on a plane or in space.

    Make sure your body is waterproof as this method involves submerging your body in water. If the body is hollow or water can penetrate into it, then you will not be able to accurately determine its volume using this method. If the body absorbs water, make sure the water will not damage it. Do not immerse electrical or electronic objects in water as this may result in injury. electric shock and / or damage to the item itself.

    • If possible, seal the body in a waterproof plastic bag (after letting it air out). In this case, you will calculate a fairly accurate value for the volume of the body, since the volume of the plastic bag is likely to be small (compared to the volume of the body).

    Find the container that holds the body, the volume of which you are calculating. If you are measuring the volume of a small object, use a graduated volumetric beaker. Otherwise, find a container whose volume can be easily calculated, for example, a container in the form rectangular parallelepiped, a cube or a cylinder (a glass can also be considered a cylindrical container).

    • Take a dry towel to place the body pulled out of the water on it.

  • Fill the container with water so that you can completely submerge your body, but leave enough space between the surface of the water and the top edge of the container. If the base of the body is irregular, such as rounded bottom corners, fill the container so that the surface of the water reaches a part of the body of the correct shape, such as straight rectangular walls.

    Mark the water level. If the water container is clear, mark the level on the outside of the container with a waterproof marker. If not, mark the water level on the inside of the container using colored adhesive tape.

    Submerge your body completely in water. If it absorbs water, wait at least thirty seconds and then pull the body out of the water. The water level should drop as some of the water is in the body. Remove the marks (marker or duct tape) about the previous water level and mark the new level. Then submerge the body in water again and leave it there.

    If the body is floating, attach a heavy object to it (as a sinker) and continue calculating with it. After that, repeat the calculations exclusively with the sinker to find its volume. Then subtract the lead volume from the body volume with the weight attached to find the body volume.

    • When calculating the volume of a lead, attach to it what you used to attach the lead to the body in question (for example, tape or pins).

  • Mark the water level with the body immersed in it. If you are using a measuring cup, record the water level according to the scale on the glass. Now you can pull the body out of the water. You probably shouldn't leave an item underwater for more than a couple of minutes, as the water can negatively affect it otherwise.

    Know why this method works. The change in the volume of water is equal to the volume of an irregularly shaped body. The method for measuring the volume of a body using a container with water is based on the fact that when a body is immersed in a liquid, the volume of a liquid with a body immersed in it increases by the amount of the volume of the body (that is, the body displaces a volume of water equal to the volume of this body). Depending on the shape of the container with water used, there are various ways to calculate the volume of displaced water, which is equal to the volume of the body.

    Find the volume using the measuring scale of the glass. If you used a container with a measuring scale, then you should already have two values ​​of the water level (its volume) recorded. In this case, subtract the volume of water before the body is immersed from the value of the volume of water with the body immersed in it. You will get body volume.

  • Find the volume using a rectangular container. If you used a box in the shape of a rectangular parallelepiped, measure the distance between the two marks (water level before body immersion and water level after body submersion), as well as the length and width of the water container. Find the volume of displaced water by multiplying the length and width of the container, as well as the distance between the two marks (that is, you calculate the volume of a small rectangular parallelepiped). You will get body volume.

    • Do not measure the height of the water container. Measure only the distance between the two marks.
    • Use

    • - free geometric calculator will help you calculate the area or volume of relatively simple geometric shapes in two clicks. No need to search for the right formulas and make calculations on a piece of paper. Working with the program is very simple, first you need to choose what you need to calculate: the area of ​​the figure, the total surface area, or the volume. The selected shape is displayed next to the box, and the formula for calculating the desired value will be shown next to it. Initially, all results are rounded to the nearest whole part, but it is possible to change and select the required precision with which the results should be displayed. For this, options from one to ten decimal places are available.

    What can be calculated?

    • Circle - find the circumference of a known radius and the diameter of a known circle.
    • We find the area - of a circle, a sector of a circle, an ellipse, a square, a rectangle, a parallelogram, a triangle, a trapezoid, a rhombus, a torus.
    • Surface area - cube, prism, pyramid, cylinder, sphere, cone, torus.
    • Volume of figures - cube, cuboid, prism, pyramid, cylinder, sphere, cone, torus, truncated cone, barrel.

    Volume formula is necessary to calculate the parameters and characteristics of a geometric figure.

    Shape volume is a quantitative characteristic of the space occupied by a body or substance. In the simplest cases, the volume is measured by the number of unit cubes that fit in the body, that is, cubes with an edge equal to a unit of length. The volume of the body or the capacity of the vessel is determined by its shape and linear dimensions.

    Volumes of geometric shapes.
    Figure Formula Drawing

    Parallelepiped.

    Rectangular volume parallelepiped

    Cylinder.

    Volume cylinder equal to the product of the area of ​​the base and the height.

    The volume of the cylinder is equal to the product of pi (3.1415) and the square of the base radius by the height.

    Pyramid.

    Volume pyramids is equal to one third of the product of the base area S (ABCDE) and the height h (OS).

    Correct pyramid Is a pyramid, at the base of which lies regular polygon, and the height passes through the center of the inscribed circle to the base.

    Regular triangular pyramid- This is a pyramid, in which the base is an equilateral triangle and the faces are equal isosceles triangles.

    Correct quadrangular pyramid Is a pyramid with a square base and equal isosceles triangles.

    Tetrahedron Is a pyramid with all faces being equilateral triangles.

    V = (a 3 √2) / 12

    Truncated pyramid.

    The volume of the truncated pyramid is equal to one third of the product of the height h (OS) by the sum of the areas of the upper base S 1 (abcde), the lower base of the truncated pyramid S 2 (ABCDE) and the average proportional between them.

    V = 1/3 h (S 1 + √S 1 S 2 + S 2)

    Calculate volume Cuba easy - you need to multiply the length, width and height. Since the length of the cube is equal to the width and equal to the height, the volume of the cube is s 3.

    Cone Is a body in Euclidean space, obtained by combining all rays emanating from one point (vertices cone) and passing through a flat surface.

    Frustum it will turn out if a section is drawn in a cone parallel to the base.

    V = 1/3 πh (R 2 + Rr + r 2)

    Volume balls one and a half times less than the volume of the cylinder described around it.

    Prism.

    Volume prisms is equal to the product of the area of ​​the base of the prism, by the height.

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