The volume of a cuboid is `1728 cm^3`.If height of the cuboid is 12 cm, then find area of its base,

Options

A. `36cm^2`
B. `144 cm^2`
C. `48cm^2`
D. `64cm^2`

Answer

To find the area of the base of the cuboid given its volume and height, we can follow these steps:

### Step 1: Understand the formula for the volume of a cuboid.
The volume \( V \) of a cuboid can be calculated using the formula:
\[ V = \text{length} \times \text{breadth} \times \text{height} \]

### Step 2: Substitute the known values into the formula.
We know the volume \( V = 1728 \, \text{cm}^3 \) and the height \( h = 12 \, \text{cm} \). We can substitute these values into the volume formula:
\[ 1728 = \text{length} \times \text{breadth} \times 12 \]

### Step 3: Rearrange the formula to find the area of the base.
The area of the base \( A \) of the cuboid is given by:
\[ A = \text{length} \times \text{breadth} \]
From the volume formula, we can express the area of the base in terms of the volume and height:
\[ A = \frac{V}{h} \]

### Step 4: Calculate the area of the base.
Substituting the known values into the rearranged formula:
\[ A = \frac{1728}{12} \]
Now, performing the division:
\[ A = 144 \, \text{cm}^2 \]

### Final Answer:
The area of the base of the cuboid is \( 144 \, \text{cm}^2 \).

---