Help your students prepare for their Maths GCSE with this free surface area worksheet of 44 questions and answers
The surface area of a 3D shape is the total area of all of the faces that make up its surface. For example, in order to calculate the surface area of a cube we need to work out the area of one of the square faces of a cube and multiply this by 6 to find the total surface area (because a cube has 6 square faces).
We can also calculate the surface area of more complex prisms (solid shapes with flat faces and constant cross-sections). For example, to find the surface area of cuboids (also known as rectangular prisms, as the cross-section of a cuboid is a rectangle) it is useful to draw its net. Then mark on the dimensions of the cuboid and calculate the area of each rectangular face before summing to find the total surface area. To find the surface area of a triangular prism we use the formula for area of a triangle to calculate the surface area of the two cross-sectional faces, then add together with the area of the three rectangular faces.
There are also formulae for curved surface areas of cones and spheres which are given in GCSE assessments. Students may be asked to work with fractions of a sphere, such as hemispheres or quarter-spheres.
Students are also expected to work out the total surface area of compound shapes which are shapes made from two or more simple 3D shapes. It’s important to think carefully about which faces make up the outside of a compound shape, for example, for a hemisphere stacked on top of a cylinder, one circular face of both the hemisphere and the cylinder will no longer be on the outside surface of the compound shape. Compound shape problems are often posed as word problems relating to real life scenarios.
Care must be taken when working with decimals and surface area of 3D shapes and it is important to only round answers at the end of a calculation.
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