VOLUME

Volume is the quantity of three-dimensional space enclosed by some closed boundary, for example, the space that a substance (solid, liquid, gas, or plasma) or shape occupied or contained. Volume is often quantified numerically using the SI derived unit, the cubic meter (m³). The volume of a container is generally understood to be the capacity of the container, i. e. the amount of fluid (gas or liquid) that the container could hold, rather than the amount of space the container itself displaces.

The volume of a solid (whether regularly or irregularly shaped) can be determined by fluid displacement. Displacement of liquid can also be used to determine the volume of a gas. The combined volume of two substances is usually greater than the volume of one of the substances. 

cube = a ³
rectangular prism = l b h
triangle = (1/2)b h l

cylinder = b h = ∏ r ² h
pyramid = (1/3) b h =  (1/3) h w l
cone = (1/3) b h = (1/3)∏ r ² h
sphere = (4/3) ∏ r ³


 

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3D Shapes I Know (song for kids)

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Three-dimensional shapes

A three-dimensional figure is a figure that has depth, width, and height. Three-dimensional geometry, or space geometry, is used to describe the buildings we live and work in, the tools we work with, and the objects we create. There are many different types of three-dimensional figures.

Prisms have flat surfaces, called faces. The faces meet to form edges. The edges meet at corners called vertices. (A single corner is called a vertex.)

Bases are used to name prisms. For example, a rectangular solid, or rectangular prism, is a three-dimensional solid with a rectangle for a base.

Think of a rectangular solid as being made of rectangles and squares. It has six faces.
A cube is a special type of rectangular solid. In a cube, all the faces are squares.

 

A pyramid has a quadrilateral for a base and triangles for sides. It has four triangular faces sharing a common vertex. In other words, a pyramid always comes to a point. Sometimes, the base is also a triangle, which gives the pyramid four faces.

Like a pyramid, a cone is a three-dimensional figure that also comes to a point. It has one circular base and a vertex that is not on the base.

A sphere is one of the most familiar three-dimensional shapes. It has no flat surfaces. You live on Earth—one large sphere! A sphere is made when you twirl a circle around one of its diameters. Like a circle, all the points of a sphere are at the same distance from its center.

A cylinder is a three-dimensional figure that has two parallel, congruent bases. Both bases are circles. If you've seen the stockpiles of canned food at a food drive, you've encountered cylinders.

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2-D & 3-D shapes

 Lets us learn more about 2-dimensional & 3-dimensional shapes, just click  http://www.bgfl.org/custom/resources_ftp/client_ftp/ks2/maths/3d/index.htm

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Area

Area is a quantity that expresses the extent of a two-dimensional shape in the plane. Area can be understood as the amount of material with a given thickness that would be necessary to fashion a model of the shape, or the amount of paint necessary to cover the surface with a single coat.
The area of a shape can be measured by comparing the shape to squares of a fixed size^. In the International System of Units (SI), the standard unit of area is the square metre (written as m²), which is the area of a square whose sides are one metre long.


square = a ²
rectangle = b h
parallelogram = bh
trapezoid = h/2 (a + b)

circle = ∏ r ²





 

triangle =

one half times the base length times the height of the triangle

  

equilateral triangle =

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Perimeter

A perimeter is a path that surrounds an area.

Perimeter of square = a + a + a + a = 4a

Perimeter of rectangle = (a+a) + (b+b) = 2a + 2b

Perimeter of triangle = a + b + c

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2D Shapes I Know- (song for kids)

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Identify the sides of 2-D shapes

A square has 4 straight sides. All the sides are equal in length.

A rectangle has 4 straight sides. The opposite sides are equal in length.

A triangle has 3 straight sides. The sides can be equal or different in length.         

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TWO-DIMENSIONAL SHAPE

 Examples of 2D shapes

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INTRODUCTION

For many years, people are told stories by drawing and painting the pictures. Therefore, SHAPE & SPACE are the basic of geometry. They play a very important role in our daily life ~
Shapes with no thickness, which have just length and width are known as two-dimensional shapes. The most common objects that we see and handle everyday are those with three-dimensions which are called solid shapes.

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Oswald Veblen said: "MATHEMATICS is one of the essential emanations of the human spirit, a thing to be valued in and for itself, like art or poetry. " So, MATHEMATICS is really important !

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