The total surface area of a cube is `253.5 cm^(2)`. Find its side (in cm).

Options

A. a.`7.5`
B. b.`5.5`
C. c.`6.5`
D. d.`8.5`

Answer

To find the side 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 (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 know from the problem that the total surface area of the cube is \( 253.5 \, \text{cm}^2 \). Therefore, we can write the equation:
\[ 6a^2 = 253.5 \]

### Step 3: Solve for \( a^2 \).
To isolate \( a^2 \), divide both sides of the equation by 6:
\[ a^2 = \frac{253.5}{6} \]

### Step 4: Calculate \( \frac{253.5}{6} \).
Now, perform the division:
\[ a^2 = 42.25 \]

### Step 5: Find \( a \) by taking the square root of \( a^2 \).
To find the side length \( a \), take the square root of both sides:
\[ a = \sqrt{42.25} \]

### Step 6: Calculate \( \sqrt{42.25} \).
Now, calculate the square root:
\[ a = 6.5 \]

### Step 7: State the final answer.
Thus, the length of the side of the cube is:
\[ \boxed{6.5 \, \text{cm}} \]

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