The area of three consecutive faces of a cuboid are ` 12 cm^(2)` . `20 cm^(2) and 15 cm^(2)`, then the volume ( in ` cm^(3)`) of the cuboid is

Options

A. 3600
B. 100
C. 80
D. 60

Answer

To find the volume of the cuboid given the areas of its three consecutive faces, we can follow these steps:

### Step 1: Assign Variables
Let:
- Length = \( l \)
- Breadth = \( b \)
- Height = \( h \)

From the problem, we have the following equations based on the areas of the faces:
1. \( l \times b = 12 \) (Area of face 1)
2. \( b \times h = 20 \) (Area of face 2)
3. \( h \times l = 15 \) (Area of face 3)

### Step 2: Multiply the Equations
To find the volume \( V \) of the cuboid, we know that:
\[ V = l \times b \times h \]

We can find \( (l \times b \times h)^2 \) by multiplying the three equations:
\[ (l \times b) \times (b \times h) \times (h \times l) = 12 \times 20 \times 15 \]
This simplifies to:
\[ (l \times b \times h)^2 = 12 \times 20 \times 15 \]

### Step 3: Calculate the Right Side
Now, we calculate \( 12 \times 20 \times 15 \):
\[ 12 \times 20 = 240 \]
\[ 240 \times 15 = 3600 \]
Thus,
\[ (l \times b \times h)^2 = 3600 \]

### Step 4: Take the Square Root
To find \( l \times b \times h \), we take the square root of both sides:
\[ l \times b \times h = \sqrt{3600} \]
Calculating the square root:
\[ \sqrt{3600} = 60 \]

### Step 5: Conclusion
Therefore, the volume \( V \) of the cuboid is:
\[ V = 60 \, \text{cm}^3 \]