Find the volume of a cube whose diagonal is 17.32 metre.

Answer

To find the volume of a cube whose diagonal is 17.32 meters, we can follow these steps:

### Step 1: Understand the relationship between the side length and the diagonal of a cube.
The diagonal \( d \) of a cube can be expressed in terms of its side length \( a \) using the formula:
\[ d = a \sqrt{3} \]

### Step 2: Substitute the given diagonal into the formula.
We know that the diagonal \( d \) is 17.32 meters. Therefore, we can set up the equation:
\[ 17.32 = a \sqrt{3} \]

### Step 3: Solve for the side length \( a \).
To find \( a \), we rearrange the equation:
\[ a = \frac{17.32}{\sqrt{3}} \]

### Step 4: Calculate \( \sqrt{3} \).
The approximate value of \( \sqrt{3} \) is 1.732. Now substitute this value into the equation:
\[ a = \frac{17.32}{1.732} \]

### Step 5: Perform the division.
Calculating this gives:
\[ a \approx 10 \text{ meters} \]

### Step 6: Calculate the volume of the cube.
The volume \( V \) of a cube is given by the formula:
\[ V = a^3 \]
Substituting the value of \( a \):
\[ V = 10^3 = 1000 \text{ cubic meters} \]

### Final Answer:
The volume of the cube is \( 1000 \) cubic meters.

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