![]() Examples of Surface Area Calculations Cube You can find more detail about units of measurement on our page Systems of Measurement. You therefore work out the area of each face, and then add them together.Īs with flat shapes, the surface area of a solid is expressed in square units: cm 2, inches 2, m 2 and so on. You can use your knowledge about the area of two-dimensional shapes to calculate the surface area of a three-dimensional shape, since each face or side is effectively a two-dimensional shape. Surface Area Our page on Calculating Area explains how to work out the area of two-dimensional shapes and you need to understand these basics in order to calculate the surface area of three-dimensional shapes.įor three-dimensional shapes, we talk about surface area, to avoid confusion. There are also more complex forms of tori. Shaped like a ring, a tyre or a doughnut, a regular ring torus is formed by revolving a smaller circle around a larger circle. Every point on the surface of a sphere is an equal distance to the centre of the sphere. Shaped like a ball or a globe a sphere is a completely round object. A cone is similar to a pyramid but distinct as a cone has a single curved side and a circular base. ![]() The side of the cone tapers smoothly to the apex. Although similar, cylinders are not prisms as a prism has (by definition) parallelogram, flat sides.Ī cone has a circular or oval base and an apex (or vertex). Cylinders have two identical ends of either a circle or an oval. Common Three-Dimensional Shapes with Curves:Ī cylinder has the same cross-section from one end to the other. In geometry the most common curved solids are cylinders, cones, spheres and tori (the plural for torus). Many of the objects around you will include at least some curves. Furthermore, a pyramid can have an apex in the direct centre of its base, a Right Pyramid, or can have the apex off centre when it's an Oblique Pyramid. What is a Pyramid?Ī pyramid is a polyhedron with a polygon base that connects to an apex (top point) with straight sides.Īlthough we tend to think of pyramids with a square base, like the ones that the ancient Egyptians built, they can in fact have any polygon base, regular or irregular. However the sides of anti-prisms are made up of triangles and not parallelograms. The sides of a prism are parallelograms - four-sided shapes with two pairs of sides of equal length.Īntiprisms are similar to regular prisms in that, their ends match. If you cut a prism anywhere along its length, parallel to an end, its cross-section is the same - you would end up with two prisms. What is a Prism?Ī prism is any polyhedron that has two matching ends and flat sides. See the diagram above for an illustration of each of these regular polyhedrons. Icosahedron with twenty equilateral triangle faces.Dodecahedron with twelve pentagon faces.Octahedron with eight equilateral triangle faces. ![]()
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