A teak wood log is first in the form a cuboid of length 2.3 m, width 0.75 m and of a certain thickness. Its volume is `1.104 m^(3)`. How many rectangular planks for size `2.3 m xx 0.75 m xx 0.04` m can be cut from the cuboid ?

Options

A. 16
B. 64
C. 68
D. 4

Answer

To solve the problem of how many rectangular planks can be cut from a teak wood log, we need to follow these steps:

### Step 1: Calculate the volume of the cuboid (teak wood log)
The volume of the cuboid is already given in the problem:
\[ \text{Volume of the cuboid} = 1.104 \, m^3 \]

### Step 2: Calculate the volume of one rectangular plank
The dimensions of one rectangular plank are given as:
- Length = 2.3 m
- Width = 0.75 m
- Thickness = 0.04 m

To find the volume of one plank, we use the formula for the volume of a cuboid:
\[ \text{Volume of one plank} = \text{Length} \times \text{Width} \times \text{Thickness} \]

Substituting the values:
\[ \text{Volume of one plank} = 2.3 \, m \times 0.75 \, m \times 0.04 \, m \]

Calculating this:
\[ \text{Volume of one plank} = 2.3 \times 0.75 \times 0.04 \]
\[ = 0.069 \, m^3 \]

### Step 3: Determine the number of planks that can be cut from the cuboid
Let \( n \) be the number of planks that can be cut from the cuboid. The total volume of the planks must equal the volume of the cuboid:
\[ n \times \text{Volume of one plank} = \text{Volume of the cuboid} \]

Substituting the known volumes:
\[ n \times 0.069 \, m^3 = 1.104 \, m^3 \]

### Step 4: Solve for \( n \)
To find \( n \), we rearrange the equation:
\[ n = \frac{1.104 \, m^3}{0.069 \, m^3} \]

Calculating this:
\[ n = \frac{1.104}{0.069} \]
\[ n \approx 16 \]

### Conclusion
The number of rectangular planks that can be cut from the cuboid is:
\[ n = 16 \]