The total surface area of a cube is 726 `cm^(2)`. What is the volume of this cube?

Options

A. 1231 `cm^(3)`
B. 1331 `cm^(3)`
C. 1431 `cm^(3)`
D. 1531 `cm^(3)`

Answer

To solve the problem of finding the volume of a cube given its total surface area, we can follow these steps:

### Step 1: Understand the formula for the total surface area of a cube.
The total surface area \( S \) of a cube is given by the formula:
\[ S = 6A^2 \]
where \( A \) is the length of one side of the cube.

### Step 2: Set up the equation using the given total surface area.
We are given that the total surface area of the cube is \( 726 \, cm^2 \). Therefore, we can set up the equation:
\[ 6A^2 = 726 \]

### Step 3: Solve for \( A^2 \).
To find \( A^2 \), divide both sides of the equation by 6:
\[ A^2 = \frac{726}{6} \]
Calculating the right side:
\[ A^2 = 121 \]

### Step 4: Solve for \( A \).
Now, take the square root of both sides to find \( A \):
\[ A = \sqrt{121} = 11 \, cm \]

### Step 5: Calculate the volume of the cube.
The volume \( V \) of a cube is given by the formula:
\[ V = A^3 \]
Substituting the value of \( A \):
\[ V = 11^3 \]
Calculating \( 11^3 \):
\[ V = 1331 \, cm^3 \]

### Final Answer:
The volume of the cube is \( 1331 \, cm^3 \).

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