Volume and surface area formulas

10 formulas · what each one means · a free lesson for each

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Volume and surface area

Rectangular box

V = lwh SA = 2lw + 2lh + 2wh

Cube

V = s³ SA = 6s²

Prism

V = Bh

B is the area of the end shape, h the length between the ends.Lesson: Prisms →

Cylinder

V = πr² h SA = 2πr² + 2πrh

Two circles plus the curved side (a rectangle when unrolled).Lesson: Volume and surface area →

Pyramid

V = 13Bh

One third of the prism with the same base and height.Lesson: Pyramids →

Cone

V = 13πr² h SA = πr² + πrl

l is the slant height (side, from tip to edge).Lesson: Cones →

Sphere

V = 43πr³ SA = 4πr²

Hemisphere

V = 23πr³ SA = 3πr²

Half a sphere plus the flat circle (2πr² + πr²).Lesson: Spheres and hemispheres →

Frustum

V = big cone − small cone

Similar solids

lengths × k, areas × k², volumes × k³