A certain quantity of wood costs `Rs. 250 "per "m^(3)`. A solid cubical block of such wood is bougth for `Rs. 182.25.` Calculate the volume of the block and edge of the cube.

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Determine the volume of wood purchased
The cost of wood is given as Rs. 250 per cubic meter. The total amount spent on the wood is Rs. 182.25.

To find the volume of wood purchased, we can use the formula:
\[ \text{Volume} = \frac{\text{Total Cost}}{\text{Cost per cubic meter}} \]

Substituting the values:
\[ \text{Volume} = \frac{182.25}{250} \]

### Step 2: Calculate the volume
Now, we will perform the division:
\[ \text{Volume} = \frac{182.25}{250} = 0.729 \, \text{m}^3 \]

### Step 3: Relate volume to the edge of the cube
The volume \( V \) of a cube is given by the formula:
\[ V = a^3 \]
where \( a \) is the length of an edge of the cube.

### Step 4: Solve for the edge length
We know the volume \( V \) is 0.729 m³. Therefore, we can set up the equation:
\[ a^3 = 0.729 \]

To find \( a \), we take the cube root of both sides:
\[ a = \sqrt[3]{0.729} \]

### Step 5: Calculate the edge length
Now we calculate the cube root:
\[ a = 0.9 \, \text{m} \]

### Final Results
- The volume of the block is \( 0.729 \, \text{m}^3 \).
- The edge length of the cube is \( 0.9 \, \text{m} \).