Question:
A cube has a surface area of 54 square units. What is the volume of the cube?
A cube has a surface area of 54 square units. What is the volume of the cube?
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To find the volume of a cube, first calculate the side length from the surface area using \( A = 6s^2 \), then use the formula \( V = s^3 \) to find the volume.
Updated On: Oct 6, 2025
- \( 27 \)
- \( 36 \)
- \( 45 \)
- \( 54 \)
- \( 64 \)
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The Correct Option is A
Solution and Explanation
The surface area \( A \) of a cube is given by the formula:
\[
A = 6s^2,
\]
where \( s \) is the side length of the cube.
Step 1: Given the surface area \( A = 54 \), we substitute into the formula:
\[
6s^2 = 54.
\]
Step 2: Solve for \( s^2 \):
\[
s^2 = \frac{54}{6} = 9
\Rightarrow
s = 3. \] Step 3: The volume \( V \) of the cube is given by: \[ V = s^3 = 3^3 = 27. \] Thus, the volume of the cube is \( 27 \).
\Rightarrow
s = 3. \] Step 3: The volume \( V \) of the cube is given by: \[ V = s^3 = 3^3 = 27. \] Thus, the volume of the cube is \( 27 \).
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