The surface area of the three coterminus faces of a cuboid are 6, 15 and 10 `cm^(2)` respectively. The volume of the cuboid is

Options

A. ` 30 cm^3`
B. `40cm^3`
C. `20cm^3`
D. `35cm^3`

Answer

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

### Step-by-Step Solution:

1. **Identify the Given Areas**:
Let the areas of the three coterminous faces of the cuboid be:
- Area 1 (length × breadth) = \( A_1 = 6 \, \text{cm}^2 \)
- Area 2 (breadth × height) = \( A_2 = 15 \, \text{cm}^2 \)
- Area 3 (height × length) = \( A_3 = 10 \, \text{cm}^2 \)

2. **Set Up the Equations**:
From the areas, we can set up the following equations:
- \( lb = 6 \) (1)
- \( bh = 15 \) (2)
- \( hl = 10 \) (3)

3. **Multiply the Equations**:
To find the volume, we need to multiply all three equations:
\[ (lb) \times (bh) \times (hl) = 6 \times 15 \times 10 \]
This gives:
\[ (lbh)^2 = 6 \times 15 \times 10 \]

4. **Calculate the Right Side**:
Calculate \( 6 \times 15 \times 10 \):
\[ 6 \times 15 = 90 \]
\[ 90 \times 10 = 900 \]
So, we have:
\[ (lbh)^2 = 900 \]

5. **Take the Square Root**:
To find \( lbh \):
\[ lbh = \sqrt{900} = 30 \]

6. **Conclusion**:
The volume of the cuboid is:
\[ \text{Volume} = lbh = 30 \, \text{cm}^3 \]

### Final Answer:
The volume of the cuboid is \( 30 \, \text{cm}^3 \).