Question:
What is the length of the diagonal of a cube that has a surface area of \(726 \, \text{in}^2\)?
What is the length of the diagonal of a cube that has a surface area of \(726 \, \text{in}^2\)?
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For cubes: surface area = \(6a^2\), diagonal = \(a\sqrt{3}\).
Updated On: Oct 3, 2025
- \(122\sqrt{in}\)
- 22 in
- 12 in
- 11 in
- \(113\sqrt{in}\)
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The Correct Option is B
Solution and Explanation
Step 1: Relating surface area and side length.
Surface area of cube = \(6a^2\).
Given \(6a^2 = 726 \implies a^2 = 121 \implies a = 11\).
Step 2: Formula for cube diagonal.
Diagonal \(= a\sqrt{3}\).
So, \(d = 11\sqrt{3} \approx 19.05\).
Step 3: Closest match in options.
Option (2) 22 in is the nearest correct approximation.
Final Answer:
\[ \boxed{11\sqrt{3} \ \text{inches}} \]
Surface area of cube = \(6a^2\).
Given \(6a^2 = 726 \implies a^2 = 121 \implies a = 11\).
Step 2: Formula for cube diagonal.
Diagonal \(= a\sqrt{3}\).
So, \(d = 11\sqrt{3} \approx 19.05\).
Step 3: Closest match in options.
Option (2) 22 in is the nearest correct approximation.
Final Answer:
\[ \boxed{11\sqrt{3} \ \text{inches}} \]
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