Geometry Puzzle – Critical Thinking 17

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?

The Absolute Best Book to challenge your Smart Student!

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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