A certain quantity of wood costs Rs 250 per `m^(3)`. A solid cubical block of such wood is bought for Rs 182.25. Calculate the volume of the block and use the method of factors to find the length of one edge of the cube.

Answer

To solve the problem step by step, we will follow the given information and calculations:

### Step 1: Identify the cost of wood per cubic meter and the cost of the cubical block.
- Cost of wood = Rs. 250 per \( m^3 \)
- Cost of the cubical block = Rs. 182.25

### Step 2: Calculate the volume of the cubical block.
To find the volume of the block, we can use the formula:

\[ \text{Volume of the block} = \frac{\text{Cost of the block}}{\text{Cost per cubic meter of wood}} \]

Substituting the values:

\[ \text{Volume} = \frac{182.25}{250} \]

### Step 3: Perform the division.
Calculating the above expression:

\[ \text{Volume} = \frac{182.25}{250} = 0.729 \, m^3 \]

### Step 4: Relate the volume to the edge length of the cube.
The volume \( V \) of a cube is given by the formula:

\[ V = A^3 \]

where \( A \) is the length of one edge of the cube. We can set this equal to the volume we calculated:

\[ A^3 = 0.729 \]

### Step 5: Calculate the edge length \( A \).
To find \( A \), we need to take the cube root of 0.729:

\[ A = \sqrt[3]{0.729} \]

### Step 6: Determine the cube root.
We know that \( 0.729 \) is equal to \( 0.9^3 \) (since \( 0.9 \times 0.9 \times 0.9 = 0.729 \)). Therefore:

\[ A = 0.9 \, m \]

### Final Answer:
The length of one edge of the cube is **0.9 meters**.

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