The total surface area of a cube is `73.5 cm^(2)`. Find its side (in cm.).

Options

A. `3.5`
B. `4.5`
C. `7.5`
D. `5.5`

Answer

To find the side of the 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 (TSA) of a cube is given by the formula:
\[ \text{TSA} = 6a^2 \]
where \( a \) is the length of a 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 \( 73.5 \, \text{cm}^2 \). Therefore, we can set up the equation:
\[ 6a^2 = 73.5 \]

### Step 3: Solve for \( a^2 \).
To find \( a^2 \), we divide both sides of the equation by 6:
\[ a^2 = \frac{73.5}{6} \]

### Step 4: Perform the division.
Calculating \( \frac{73.5}{6} \):
\[ 73.5 \div 6 = 12.25 \]
So, we have:
\[ a^2 = 12.25 \]

### Step 5: Take the square root to find \( a \).
Now, we take the square root of both sides to find \( a \):
\[ a = \sqrt{12.25} \]

### Step 6: Calculate the square root.
Calculating \( \sqrt{12.25} \):
\[ a = 3.5 \, \text{cm} \]

### Final Answer:
The side of the cube is \( 3.5 \, \text{cm} \).

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