The surface area of a cube is 600 sq m. Its diagonal is

Options

A. `10 sqrt3 cm`
B. `5 sqrt3 cm`
C. `4 sqrt3 cm`
D. `10 sqrt2 cm`

Answer

To find the diagonal of a cube given its surface area, we can follow these steps:

### Step 1: Understand the Surface Area of a Cube
The 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
We know from the problem that the surface area of the cube is 600 sq m. Therefore, we can set up the equation:
\[ 6a^2 = 600 \]

### Step 3: Solve for \( a^2 \)
To find \( a^2 \), we divide both sides of the equation by 6:
\[ a^2 = \frac{600}{6} = 100 \]

### Step 4: Solve for \( a \)
Now, we take the square root of both sides to find \( a \):
\[ a = \sqrt{100} = 10 \text{ m} \]

### Step 5: Find the Diagonal of the Cube
The formula for the diagonal \( d \) of a cube is given by:
\[ d = a\sqrt{3} \]
Substituting the value of \( a \):
\[ d = 10\sqrt{3} \text{ m} \]

### Final Answer
Thus, the diagonal of the cube is:
\[ 10\sqrt{3} \text{ m} \]

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