3D Shapes and Their Properties

Basic Terminology

A 3D shape is a geometric figure that has length, breadth, and depth.
3D shapes have faces, which are the flat surfaces of the shape, edges, the lines where the faces meet, and vertices, the points where the edges meet.
The surface area of a shape is the total area of all its faces.
The volume of a shape is the space it takes up, calculated in cubic units.

A prism is a shape with two parallel and congruent faces, known as the bases, connected by parallelogram faces.
A cylinder has two parallel circular bases and one curved face.
A cone has one circular base and one curved face leading to a point, or vertex.
A pyramid has a polygonal base and triangular faces that meet at a single vertex.
A sphere is a shape with all points the same distance from the centre. It has one curved face and no edges or vertices.
A cube is a special type of prism where all faces are squares.
A cuboid is a prism with all faces as rectangles.

The surface area of a shape can be calculated by adding the areas of all its faces.
The volume of a prism or cylinder can be calculated using the formula Area of base x height.
The volume of a cone or pyramid can be calculated using the formula 1/3 x Area of base x height.
The volume of a sphere can be calculated using the formula 4/3πr³, where r is the radius.
In a prism, the cross sections parallel to the base are congruent.
In a cylinder, the cross sections parallel to the base are all circles of the same size.
The edges of a cube are all the same length, and the angles between any two edges are right angles.
In a cuboid, opposite faces are equal in area and the angles between any two edges are right angles.

This overview of 3D shapes and their properties should provide a firm foundation for understanding and working with these shapes in various contexts.