Question

The total surface area of a cube is \(54\text{ cm}^2\), then its side is ___ cm.

• A. 6
• B. 2
• C. 3
• D. 4

Hint:

Important cube formulas: \[ \boxed{\text{Total Surface Area}=6a^2} \] \[ \boxed{\text{Volume}=a^3} \] where \(a\) is the side of the cube.

Answer 1

The Correct Option is C

Concept: The total surface area (TSA) of a cube of side \(a\) is \[ \boxed{\text{TSA}=6a^2.} \]

Step 1: Form the equation.
Given, \[ 6a^2=54. \]

Step 2: Solve for the side.
Divide both sides by \(6\): \[ a^2=9. \] Taking the positive square root, \[ a=3\text{ cm}. \]

Step 3: Verification.
Substitute \(a=3\): \[ 6(3)^2=6\times9=54\text{ cm}^2, \] which matches the given surface area.

Step 4: Final conclusion.
Hence, the side of the cube is \[ \boxed{3\text{ cm}.} \]