The total surface area of a cube is `337.5 cm^(2)`. Find its side (in cm.)

Options

A. 8.5
B. 6.5
C. 5.5
D. 7.5

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 that the total surface area is \( 337.5 \, \text{cm}^2 \). Therefore, we can set up the equation:
\[ 6a^2 = 337.5 \]

### Step 3: Solve for \( a^2 \).
To isolate \( a^2 \), divide both sides of the equation by 6:
\[ a^2 = \frac{337.5}{6} \]

### Step 4: Calculate \( \frac{337.5}{6} \).
Perform the division:
\[ a^2 = 56.25 \]

### Step 5: Find \( a \) by taking the square root of both sides.
To find the side length \( a \), take the square root of \( 56.25 \):
\[ a = \sqrt{56.25} \]

### Step 6: Calculate \( \sqrt{56.25} \).
Calculating the square root:
\[ a = 7.5 \, \text{cm} \]

### Final Answer:
The side of the cube is \( 7.5 \, \text{cm} \).

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