# Geometry Puzzle – Critical Thinking 17

If you are a math teacher, you can move beyond the norm in your math classroom and challenge students to think critically by this kind of critical thinking challenges!

## Challenge:

The volume of a cube is one third of the total surface area of the cube. What is the sum of all edges of the cube?

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The correct answer is 24.

A cube has 12 edges. The formula for the volume and surface area of a cube are:

V = S\(^3\) SA = 6S\(^2\)

The volume of a cube is one-third of the total surface area of the cube. Thus:

S\(^3= \frac{1}{3}\)6S\(^2\)

Remove S\(^2\) from both sides and solve for S.

S = \(\frac{1}{3}\)6 = 2

One side of the cube is 2. The sum of all edges is

2 × 12 = 24

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