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Geometry reference

Surface Area and Volume Formula Handout

Print a reference for cubes, rectangular and general prisms, cylinders, pyramids, cones and spheres, with definitions and formula assumptions.

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Use the stated right-solid or regular-pyramid assumptions. Surface area uses square units; volume uses cubic units.

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Reference handout

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Reference handout
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Match the formula to its assumptions

The handout separates general right-prism and pyramid facts from shortcuts that require a right solid or a regular pyramid with one common face slant height.

Learning objective

What this activity builds

Select a valid surface area or volume formula and interpret every variable.

Worked example

Which height goes into a pyramid volume formula?

The perpendicular height h, in V = Bh/3.

The face slant height is used for triangular-face areas. It is not the perpendicular distance from the apex to the base.

Teaching notes

Make the practice count

  • Identify the base and calculate its area B first.
  • Use each triangular face area for a general pyramid.
  • Use calculator pi and round only the final result when an approximation is required.

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3 reference pages
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Math SheetNameScoreTeacherDateSolid Figures Formula ReferenceUse the stated assumptions for each formula. Area is measured in square units and volume in cubic units.CubeA rectangular prism with six congruent square faces.Assumption: All edges have length s.Six congruent square faces.Surface area: SA = 6s^2 (square units)Volume: V = s^3 (cubic units)s = edge lengthRectangular Prism (Cuboid)A right prism with rectangular faces.Assumption: Edges l, w and h meet at right angles.Opposite faces are congruent.Surface area: SA = 2lw + 2lh + 2wh (square units)Volume: V = lwh (cubic units)l = length; w = width; h = perpendicular heightGeneral Right PrismA solid with two congruent parallel polygonal bases joined by rectangles.Assumption: The prism is right; h is perpendicular to both bases.B is one base area and P is its perimeter.Surface area: SA = 2B + Ph (square units)Volume: V = Bh (cubic units)B = area of one base; P = base perimeter; h = perpendicular heightDiagrams are not to scale.math-sheet.comPage 1 of 3
Math SheetNameScoreTeacherDateSolid Figures Formula ReferenceUse the stated assumptions for each formula. Area is measured in square units and volume in cubic units.Right CylinderA solid with two congruent circular bases.Assumption: The cylinder is right; h is perpendicular to the bases.The lateral net is a rectangle of width 2*pi*r.Surface area: SA = 2*pi*r^2 + 2*pi*r*h (square units)Volume: V = pi*r^2*h (cubic units)r = base radius; h = perpendicular heightPyramidA solid with one polygonal base and triangular faces meeting at an apex.Assumption: h is perpendicular from the apex to the base.Assumption: SA = B + Pl/2 only for a regular pyramid with one common face slant height l.For a general pyramid, add the areas of the individual triangular faces.General surface area: SA = B + sum of triangular-face areas (square units)Regular-pyramid surface area: SA = B + Pl/2 (square units)Volume: V = Bh/3 (cubic units)B = base area; P = base perimeter; h = perpendicular height; l = face slant heightRight ConeA solid with a circular base and one apex.Assumption: The cone is right; the apex lies above the base center.l is the slant height from the apex to the base circle.Surface area: SA = pi*r^2 + pi*r*l (square units)Volume: V = pi*r^2*h/3 (cubic units)r = base radius; h = perpendicular height; l = slant heightDiagrams are not to scale.math-sheet.comPage 2 of 3
Math SheetNameScoreTeacherDateSolid Figures Formula ReferenceUse the stated assumptions for each formula. Area is measured in square units and volume in cubic units.SphereAll points in space at distance r from one center.Assumption: r is the radius.The diameter is 2r.Surface area: SA = 4*pi*r^2 (square units)Volume: V = 4*pi*r^3/3 (cubic units)r = radiusDiagrams are not to scale.math-sheet.comPage 3 of 3

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