Lateral Surface/Face

High School

Definition

A solid's surface that can be considered a face. This excludes the bases of the solid. In the case of a cylinder, for example, its lateral surface is the side of the cylinder. The top and bottom circles would not be considered a part of its lateral face.

Worked examples

\(\)Rectangular prism: lateral faces are the four rectangles forming the sides (not the top or bottom).\(\)

The lateral faces are the vertical sides; the top and bottom rectangles are bases.

\(\)Cylinder: lateral surface is the curved side (not the two circular bases).\(\)

The lateral surface wraps around the cylinder; the circles at top and bottom are excluded.

\(\)Square pyramid: lateral faces are the four triangles meeting at the apex (not the square base).\(\)

The triangular sides are lateral faces; the square bottom is the base.

Common mistakes

counting the top and bottom of a prism as lateral faces → lateral faces are only the sides; top and bottom are bases Lateral means 'side' — bases are excluded by definition.
saying a sphere has lateral faces → a sphere has one continuous surface with no bases or separate lateral faces Lateral faces apply to polyhedra and cylinders/cones, not to spheres.
including the base of a cone in its lateral surface → the cone's lateral surface is only the slanted side, not the circular base The base is never part of the lateral surface.

Where you'll use it next

You'll use lateral surface and lateral area when calculating surface area and volume of prisms, cylinders, pyramids, and cones in geometry, and later in calculus when finding surface integrals.

Found in 1 StudyPug lesson

Surface Area of Prisms: Mastering Calculations and Formulas

Grade 8 Math

Dive into the world of prism surface areas! Learn essential formulas, step-by-step calculations, and real-world applications. Perfect for students looking to excel in geometry and problem-solving.

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