Solid Figures in Geometry

What are Solid Figures?

Solid figures are three-dimensional shapes that have length, width, and height. They occupy space and have volume.

Types of Solid Figures:

1. Polyhedra

• A polyhedron is a solid figure with flat faces and straight edges.
• Examples: cube, tetrahedron, hexahedron, etc.

2. Prism

• A prism is a polyhedron with two identical faces that are parallel to each other.
• Examples: rectangular prism, triangular prism, etc.

3. Pyramid

• A pyramid is a polyhedron with a base and triangular faces that meet at the apex.
• Examples: square pyramid, triangular pyramid, etc.

4. Spherical Figures

• A sphere is a set of points equidistant from a central point called the center.
• Examples: sphere, hemisphere, etc.

5. Conical Figures

• A cone is a set of points that are equidistant from a central point called the vertex.
• Examples: cone, circular cone, etc.

6. Cylindrical Figures

• A cylinder is a set of points that are equidistant from a central axis.
• Examples: cylinder, circular cylinder, etc.

Properties of Solid Figures:

• Face: a flat surface of a solid figure.
• Edge: a line where two faces meet.
• Vertex: a point where three or more edges meet.
• Volume: the amount of space inside a solid figure.
• Surface Area: the total area of all the faces of a solid figure.

Formulas:

• Volume of a Rectangular Prism: V = lwh, where l, w, and h are the length, width, and height respectively.
• Surface Area of a Rectangular Prism: SA = 2lw + 2lh + 2wh, where l, w, and h are the length, width, and height respectively.

Solid Figures

• Three-dimensional shapes with length, width, and height that occupy space and have volume.

Types of Solid Figures

• Polyhedra: solid figures with flat faces and straight edges, examples include cube, tetrahedron, and hexahedron.
• Prism: a polyhedron with two identical faces that are parallel to each other, examples include rectangular prism and triangular prism.
• Pyramid: a polyhedron with a base and triangular faces that meet at the apex, examples include square pyramid and triangular pyramid.
• Spherical Figures: a set of points equidistant from a central point called the center, examples include sphere and hemisphere.
• Conical Figures: a set of points equidistant from a central point called the vertex, examples include cone and circular cone.
• Cylindrical Figures: a set of points equidistant from a central axis, examples include cylinder and circular cylinder.

Properties of Solid Figures

• Face: a flat surface of a solid figure.
• Edge: a line where two faces meet.
• Vertex: a point where three or more edges meet.
• Volume: the amount of space inside a solid figure.
• Surface Area: the total area of all the faces of a solid figure.

Formulas

• Volume of a Rectangular Prism: V = lwh, where l, w, and h are the length, width, and height respectively.
• Surface Area of a Rectangular Prism: SA = 2lw + 2lh + 2wh, where l, w, and h are the length, width, and height respectively.

Solid Figures

Prism

• A prism is a solid figure with two identical polygon faces (bases) connected by a rectangular solid
• Bases are polygons and can have any number of sides
• Number of faces depends on the number of sides of the base (e.g., triangular prism: 5 faces, rectangular prism: 6 faces)
• Volume calculation: base area × height

Pyramid

• A pyramid is a solid figure with a polygon base and triangular faces meeting at the apex
• Base can be any polygon, but triangular faces must be identical
• Number of faces depends on the number of sides of the base (e.g., triangular pyramid: 4 faces, square pyramid: 5 faces)
• Volume calculation: (base area × height) / 3

Cone

• A cone is a solid figure with a circular base and a curved surface tapering to a point
• Volume calculation: (base area × height) / 3
• Surface area includes base area and curved surface area

Sphere

• A sphere is a symmetrical solid figure about its center
• Every surface point is equidistant from the center
• Volume calculation: (4/3) × π × radius³
• Surface area calculation: 4 × π × radius²