**Solids Shapes (Solid geometry) in Maths & their types and Formulas**

Solids or three-dimensional forms are three-dimensional shapes with three (or more) dimensions in geometry. Solid geometry studies the characteristics, volume, and surface area of three-dimensional forms. Let us now turn our attention to the study of geometrical solids.

**Solids: Definition**

Three-dimensional forms, often known as solids, are shapes that inhabit space. Figures with three dimensions—length, breadth, and height—are also known as solid forms. A sphere, or three-dimensional form, is a ball, whereas a circle written on a sheet of paper is a two-dimensional figure. Similarly, solid shapes such as tables, chairs, notepads, or pens are all around us. Here are some solid examples and attributes of solid forms.

The geometrical figures are categorized according to their dimensions as follows:

**Zero-dimensional shape –**As the name suggests, 0-dimensional shapes are just a point.**One-dimensional shape –**A line is an example of such a shape since there is only one dimension: its length.**Two-dimensional shapes –**Such shapes have two dimensions of length and breadth. E.g., polygon, square, triangle, rectangle, circle.**Three-dimensional shapes –**Such shapes have three dimensions, i.e., length, breadth, and height. E.g., cuboid, cone, cylinder, sphere, cube, pyramid.**Higher-dimensional shapes:**Such shapes have more than three dimensions, and we will study them in higher classes.

**Solid Geometric Shapes: Some Attributes**

Some attributes of solid geometric shapes are as follows:

**Faces:** The faces of the solid figures are the single flat figures of the solid figures. It might be square, rectangular, or any other polygon.

**Edges:** The edges of solid objects are line segments between two faces where the two faces meet.

**Vertices:** The vertices are the spots where the solid figures’ edges meet. In most circumstances, three faces join at a single vertex. The plural form of a vertex is vertices.

**Solids: Types**

So let us try to understand solids from a different perspective.

Would you agree that a cube is a 3-dimensional form of a square?

Would you agree that a pyramid is a 3-dimensional form of a triangle?

Would you agree that a sphere or a cylinder is a 3-dimensional form of a circle?

You would, right!

So we can think of solids as 3-dimensional forms of 2-dimensional figures. Furthermore, this approach can simplify how we understand the properties of such solids.

**Cube : **A cube is solid with six square sides. It is a 3-dimensional figure with length, breadth, and height. However, since we know that a square has equal sides and this shape is made of 6 squares, its length = breadth = height. Imagine a Ludo Dice for a good example!

Its properties are as follows:

- 6 faces
- 12 edges
- 8 vertices
- All sides are perpendicular to each other or are at 90-degree angles.

**Cuboid: **A cuboid, also known as a rectangular prism, is a solid form of two-dimensional rectangular sides. Imagine a shoebox or a wooden box for a good example!

It has the following properties:

- Opposite faces, as well as opposite edges, are equal.
- 8 vertices
- 12 edges
- 6 faces
- All sides are perpendicular to each other or are at 90-degree angles.

**Cylinder: **The term cylinder refers to a solid object with two circular bases and a curving surface. Imagine a Coca-Cola Can for a good example!

Its properties are as follows:

- 2 edges
- 0 vertices
- 2 flare services (the top and the bottom)
- 1 curved surface

**Cone: **A cone is a solid object having one circular base attached to a curving surface and a single vertex. Imagine Ice cream waffle Cones for a good example!

Its properties are as follows:

- 1 edge
- 1 vertex
- 1 flat face
- 1 curved face

**Sphere: **A sphere is a solid that is completely spherical in form. Imagine a football!

Its properties are as follows:

- 0 vertices
- 0 edges
- 0 flat surfaces
- 1 curved surface

**Solid Formula List**

(Formula list for Solid Shapes in Maths)

Now that we know about the properties of all these solids, let’s also make a note of all its perimeters and areas.

Shape(solid shapes name) |
Volume |
Total Surface Area |

Cuboid |
l × b × h | 2 (lb + lh + hb) |

Cube |
a^{3} |
6a^{2} |

Sphere |
(4/3)πr^{3} |
4πr^{2} |

Cylinder |
πr^{2}h |
2πr(r + h) |

Cone |
(⅓)πr^{2}h |
πr(r + l) |

**Let’s also try using these formulas to solve some questions.**

**1. Calculate the surface area and volume of a cube where a side is 6 cm.
**Given that side, a = 8 cm

Cube’s volume = a

^{3}

Substituting the values, cube’s volume = 8

^{3}= 6*6*6 = 512 cm

^{3}.

Now cube’s surface area = 6a

^{2}

Substituting the values, cube’s surface area = 6*8

^{2}= 6*8*8 = 384 cm

^{2}.

**2. Find the volume of the sphere of the radius of 3 cm.
**Given that sphere’s radius, r = 3 cm

Sphere’s volume = 4/3πr

^{3}

Substituting the values, sphere’s volume = 4/3 * 22/7 * 3 * 3 * 3 = 112.75 cm

^{3}.

**3. Calculate the total surface area of a cuboid with dimensions of 6 cm × 5 cm × 9 cm.
**Given that, l = 6 cm, b = 5 and h = 9 cm.

Cuboid’s total surface area = 2 (lb + bh + hl)

Substituting the values, cuboid’s surface area = 2 (6*5 + 5*9 + 6*9) = 258 cm

^{2}.

**FAQs (Frequently Asked Questions)**

**1. Mention different types of solid shapes(solid shapes names).**

The following are the several sorts of solid forms depending on their appearance:

- Cube
- Cuboid
- Sphere
- Cylinder
- Cone
- Prism
- Pyramid

**2. State the difference between cube and cuboid.**

A cube and a cuboid are distinguished by the fact that a cube has six identical square-shaped faces, but on the other hand, a cuboid has rectangular faces. However, the cube and the cuboid have similar structures, there are some differences in faces, diagonals, and edge length.

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