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3-dimensional solids - OCRVolume and surface area

3-dimensional solids have faces, edges and vertices. Volume is the space contained within a 3D solid. Surface area is the sum of the area of each face. 3D solids can be viewed from different points.

Part ofMathsGeometry and measure

Volume and surface area

Check out the updated revision resources for GCSE Maths: Volume, with step-by-step slideshows, quizzes, practice exam questions, and more!

The volume of a solid is the space inside it.

12 cube cuboid

This cuboid contains 12 small cubes. Each small cube has a volume of 1 cm3.

Cube (1cm x 1cm x 1cm)

The volume of the cuboid is 12 cm3.

The surface area of a 3D solid is the total area of all the faces.

A cube has six faces which are all squares.

View of a cube and three of its sides

The area of one face is:

\(5 \times 5 = 25~\text{cm}^2\)

There are six faces with the same area.

The surface area of the cube is \(6 \times 25 = 150~\text{cm}^2\).