How do you find the volume and surface area of a cube?

Category: 3D Shapes »

Course: Geometry »

Relevant MM Lessons:
• Forthcoming

Cubes

Similar to spheres, the "perfect" nature of the cube means that it only has one measurement to define it - its side length. Like any 3D rectangular prism or box, its volume is the product of each of its three dimensions, $lwh$. However, since in a cube all three dimensions are the same, a cube has a volume of$$V = s^3$$where $s$ is the side length of the cube.For the surface area, we start with the fact that a single side of a cube is a square, with area $s^2$. A cube has six sides, so the total surface area is given by the formula$$S = 6s^2$$

Tips

• Remember confidently that the volume formula has an exponent of $3$ because volume is measured in "cubic units"
• Recall that dice have $6$ sides to help you remember the formula for surface area
• In application problems, be careful that sometimes we are asked to work with boxes and cubes without tops - volume doesn't change but the surface area does
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