Geometry Puzzle – Critical Thinking 17
This puzzle gives you a single condition: the volume of a cube equals one third of its total surface area. Translate that into algebra, V = (1/3) × SA, set up the cube formulas, and you can solve for the edge length in one short equation.
Key takeaways:
- For a cube of edge \( s \): volume \( V = s^3 \); total surface area \( SA = 6s^2 \).
- Translate the condition: \( V = \frac{1}{3} \cdot SA \) becomes \( s^3 = \frac{1}{3}(6s^2) = 2s^2 \).
- Divide both sides by \( s^2 \) (since \( s \neq 0 \)) to get \( s = 2 \).
- The cube has edge length 2, and its volume (8) really is one third of its surface area (24).
- Critical-thinking puzzles like this reward translation skill, not heavy computation.
If you are a math teacher, you can move beyond the norm in your math classroom and challenge students to think critically with this kind of critical thinking challenge!
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.
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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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Frequently Asked Questions
What are geometry puzzle problems?
Geometry puzzle problems give you a condition about a shape and ask you to work out a missing measurement. In this one, a cube’s volume is one third of its surface area. Writing s³ = ⅓ × 6s² = 2s² and dividing by s² gives an edge of 2. A cube has 12 edges, so they add up to 12 × 2 = 24.
Are there geometry puzzles in PDF with answers?
Yes, printable geometry puzzle sets with answer keys are widely available, and this cube challenge works well on paper with its solution. Try it before peeking: write the volume formula V = s³ and the surface area formula SA = 6s², set up the condition, and solve. Then check that a cube with edge 2 has volume 8 and surface area 24.
What is critical thinking in math class?
Critical thinking in math class means turning words into math and checking every step. This cube puzzle is a good test. Students translate one sentence into s³ = 2s², then ask whether dividing by s² is allowed. It is, because a real cube has an edge length greater than 0. That habit of justifying each move matters more than the arithmetic itself.
Are puzzles critical thinking?
Yes, the best math puzzles are critical thinking practice because they hide the method. Nothing in this cube puzzle says to write an equation, so students must decide on their own to compare V = s³ with SA = 6s². A nice extension is asking when volume and surface area are numerically equal: s³ = 6s² gives s = 6, where both equal 216.
Is math considered a puzzle?
Math is not only puzzles, but problems like this cube challenge show how puzzle-like it can be. You start with a single clue, volume equals one third of surface area, and the cube formulas do the rest. The answer, a total edge length of 24, comes from just a few steps once the clue is translated correctly.
Related Lessons You May Like
- How to find volume and surface area of cubes
- How to calculate the volume of cubes and prisms
- How to find the area of rectangles
- How to solve multi-step word problems
- How to find equivalent fractions
If your student likes puzzles like this one, Geometry for Beginners works the same kinds of relationships inside a full geometry curriculum. For the algebra you’ll lean on for setting up the equations, Pre-Algebra for Beginners fills in the foundations gently.
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