The length and breadth of a cuboidal store are in the ratio 2 : 1 and its height is 3.5 metres. If the area of its four walls (including doors) is `210 m^2` , then its volume is

Options

A. `679 m^3`
B. `700 m^3`
C. `567 m^3`
D. `1050 m^3`

Answer

To solve the problem, we will follow these steps:

### Step 1: Define the dimensions of the cuboid
Let the breadth of the cuboidal store be \( x \) meters. According to the ratio given, the length will be \( 2x \) meters.

### Step 2: Use the height of the cuboid
The height of the cuboidal store is given as \( 3.5 \) meters.

### Step 3: Calculate the area of the four walls
The formula for the area of the four walls of a cuboid is given by:
\[ \text{Area} = 2h(l + b) \]
Where:
- \( h \) is the height,
- \( l \) is the length,
- \( b \) is the breadth.

Substituting the values we have:
\[ \text{Area} = 2 \times 3.5 \times (2x + x) = 2 \times 3.5 \times 3x = 21x \]

### Step 4: Set up the equation
We know that the area of the four walls is \( 210 \, m^2 \):
\[ 21x = 210 \]

### Step 5: Solve for \( x \)
To find \( x \), divide both sides of the equation by \( 21 \):
\[ x = \frac{210}{21} = 10 \, \text{meters} \]

### Step 6: Find the length
Now that we have \( x \), we can find the length:
\[ l = 2x = 2 \times 10 = 20 \, \text{meters} \]

### Step 7: Calculate the volume of the cuboid
The volume \( V \) of a cuboid is given by the formula:
\[ V = l \times b \times h \]
Substituting the values we found:
\[ V = 20 \times 10 \times 3.5 \]

### Step 8: Perform the multiplication
Calculating the volume:
\[ V = 20 \times 10 = 200 \]
\[ V = 200 \times 3.5 = 700 \, \text{m}^3 \]

### Final Answer
The volume of the cuboidal store is \( 700 \, m^3 \).

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