The volume of a cube is numerically equal to the sum of its edges. What is the…
2019
The volume of a cube is numerically equal to the sum of its edges. What is the total surface area in square units?
Answer: A. 72 — Key idea: Let the side length of the cube be s. Volume = s³ and the sum of all edges = 12s, so set s³ = 12s. Solve the equation: s³ = 12s ⇒ s(s² − 12) = 0.…
- A.
72
- B.
12
- C.
36
- D.
144
Attempted by 17 students.
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Correct answer: A
Key idea: Let the side length of the cube be s. Volume = s³ and the sum of all edges = 12s, so set s³ = 12s.
Solve the equation: s³ = 12s ⇒ s(s² − 12) = 0. Discard s = 0, so s² = 12.
Total surface area = 6s² = 6 × 12 = 72 square units.
Answer: 72
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