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The material ingredient that makes up the observable cosmos is known as matter. All objective phenomena are understood to be founded on matter and energy. In classical physics and general chemistry, the term matter refers to any material with mass and volume that occupies space. Because it takes up space and has mass, matter is the “stuff” that makes up the cosmos. Atoms, which are made up of protons, neutrons, and electrons, make up all matter. Chemical energy is the force that holds atoms and molecules together. Everything that has mass and volume is defined as matter (takes up space). Most everyday goods that we deal with on a daily basis have mass and take up space, which is very easy to demonstrate.
Geometric Forms
The geometrical figures are categorised according to their dimensions:
A point is a zero-dimensional shape.
A one-dimensional shape is a line with only one dimension: length.
Two-dimensional shapes are figures with two dimensions: length and width. Square, triangle, rectangle, parallelogram, trapezoid, rhombus, quadrilateral, polygon, circle, and so on are examples of shapes.
Three-dimensional shapes are objects that have three dimensions: length, width, and height. Cube, cuboid, cone, cylinder, sphere, pyramid, prism, and so on.
Higher-dimensional shapes — Although there are a few shapes with dimensions greater than three, we rarely study them in middle school mathematics.
What exactly are solids?
Solids come in a variety of shapes and sizes in geometry. Solids are three-dimensional shapes with three dimensions: length, width, and height. Solids are the bodies that take up space.
Properties
A solid is defined as a group of atoms with fixed average locations in relation to one another.
Except for occasional contacts as molecules transiently approached one another, we almost completely ignored the potential energy of atom interaction when investigating gases. But this is not possible in solids: solids exist because of the potential energy of atom contact. Electrical interactions with their neighbours force the atoms of a solid to vibrate around their average location. Only in extreme circumstances do they shift their posture in relation to their neighbours. This image is undoubtedly familiar to you, but just in case it isn’t, the illustration below depicts how we perceive atoms in a solid moving.
We were able to arrive at the theory of an ‘ideal gas’ while discussing the properties of gases, which was a good approximation to the properties of real gases for many uses. Solids, on the other hand, have many fewer features that can be explained using a ‘ideal solid’ hypothesis. The variety of features that solids exhibit (for example, the distinction between metals and insulators) necessitates the creation of many simple models to serve as starting points for attempts to comprehend the behaviour of real solids.
Despite the diversity of solid features, it is vital to remember that the electrostatic coulomb force is the single force acting between atoms in all materials. The coulomb force, in combination with the various arrangements of electrons in the outer sections of the 100 or so distinct sorts of atoms, is sufficient to form the variety of solids that you see around you.
Solids Examples
Question 1: Calculate the volume and surface area of a cube with a 5 cm side.
Solution:
Side, a = 5 cm
The formula for calculating the volume of a cube is:
A cube’s volume is equal to a³ cubic units.
V = 5³
V = 5 × 5 × 5
V =125 cm³
As a result, a cube’s volume is 125 cubic centimetres.
A cube’s surface area is 6a² square units.
SA = 6(5)² cm²
SA = 6 (25)
SA = 150 cm²
As a result, a cube’s surface area is 150 square centimetres.
2nd question: Calculate the volume of a sphere with a radius of 7 cm.
Solution:
The sphere’s radius is r = 7 cm.
4/3 π r3 is the volume of a sphere.
= (4/3) × (22/7) × 7 × 7 × 7
= 4 × 22 × 7 × 7
= 4312 cm3
Question 3: Calculate the total surface area of an 8 cm x 5 cm x 7 cm cuboid.
Solution:
8 cm 5 cm 7 cm are the dimensions of a cuboid.
As a result, length = l = 8 cm.
Breadth=b=5cm
h = 7 cm = height
A cuboid’s total surface area is equal to 2(lb + bh + hl).
= 2[8(5) + 5(7) + 7(8)]
= 2(40 + 35 + 56)
= 2 × 131
= 262 cm2
Conclusion
Solid figures contain length, breadth, and height, and are three-dimensional objects. They have depth and take up space in our universe because they have three dimensions. The traits that distinguish each sort of solid figure are used to identify them.
