Question

If the total surface area of the cube is 864 cm², then its volume is

• A. 144 cm³
• B. 1728 cm³
• C. 3174 cm³
• D. 576 cm³

Answer 1

The Correct Option is B

To solve the problem, we need to find the volume of a cube whose total surface area is given as \( 864 \, \text{cm}^2 \).

1. Understanding the Surface Area of a Cube:
The total surface area \(A\) of a cube is given by:

\( A = 6a^2 \)
where \(a\) is the length of the side of the cube.

2. Substituting the Given Value:
We are given \( A = 864 \), so:

\( 6a^2 = 864 \)

3. Solving for Side Length \(a\):
Divide both sides by 6:
\( a^2 = \frac{864}{6} = 144 \)
Now take the square root:
\( a = \sqrt{144} = 12 \, \text{cm} \)

4. Calculating the Volume:
The volume \(V\) of a cube is given by:
\( V = a^3 \)
Substitute \(a = 12\):
\( V = 12^3 = 1728 \, \text{cm}^3 \)

Final Answer:
The volume of the cube is \( 1728 \, \text{cm}^3 \).