Volume and Surface Area of Prism - GCSE Maths

A prism is a 3D shape formed by stretching a 2D shape (the cross-section) into three dimensions. The defining characteristic of a prism is that it has a constant cross-section throughout its length.

The volume of a prism is calculated by multiplying the area of its cross-section by its length. Examples include triangular prisms and prisms with trapezoidal cross-sections.

For prisms with compound cross-sections, first, calculate the area of the compound 2D shape by dividing it into simpler shapes (e.g., rectangles). Then, multiply this total area by the prism's length to find the volume.

To find the surface area of a prism, you need to calculate the area of each individual face and then sum them up. This includes the two identical cross-sectional faces and all the rectangular (or other polygonal) faces forming the sides.

This section provides examples of calculating the surface area for different triangular prisms, breaking down the calculation of each face (triangles and rectangles) and summing them.

An example demonstrates calculating the surface area of a prism with a trapezoidal cross-section, including the area of the two trapezoidal ends and the various rectangular side faces.

If the volume of a prism and its cross-sectional dimensions are known, the length of the prism can be found by setting up an equation where 'Area of Cross-section × Length = Volume' and solving for the unknown length.

When the volume and length of a prism are given, and the cross-sectional area is unknown, an equation ('Area × Length = Volume') can be used to solve for the area of the cross-section.

This part explains how to find a specific dimension of the cross-section, such as the height of a triangular cross-section, when the volume and other dimensions are known. It involves expressing the cross-sectional area in terms of the unknown variable and then solving the volume equation.