The total surface area of a cuboid is `194 m^(2)`. If its length is 8 m and breadth is 6 m, then what is its volume ( in `m^(2)`)?

Options

A. 224
B. 112
C. 126
D. 168

Answer

To find the volume of the cuboid given its total surface area, length, and breadth, we can follow these steps:

### Step 1: Write down the formula for the total surface area of a cuboid.
The total surface area (TSA) of a cuboid is given by the formula:
\[ TSA = 2(lb + bh + lh) \]
where \( l \) is the length, \( b \) is the breadth, and \( h \) is the height.

### Step 2: Substitute the known values into the formula.
We know:
- Total Surface Area (TSA) = 194 m²
- Length (l) = 8 m
- Breadth (b) = 6 m

Substituting these values into the TSA formula:
\[ 194 = 2(8 \cdot 6 + 6h + 8h) \]

### Step 3: Simplify the equation.
Calculate \( 8 \cdot 6 \):
\[ 8 \cdot 6 = 48 \]
Now substitute this back into the equation:
\[ 194 = 2(48 + 6h + 8h) \]
Combine the terms:
\[ 194 = 2(48 + 14h) \]

### Step 4: Divide both sides by 2 to simplify.
\[ 97 = 48 + 14h \]

### Step 5: Solve for \( h \).
Subtract 48 from both sides:
\[ 97 - 48 = 14h \]
\[ 49 = 14h \]
Now divide by 14:
\[ h = \frac{49}{14} = 3.5 \, \text{m} \]

### Step 6: Calculate the volume of the cuboid.
The volume (V) of a cuboid is given by:
\[ V = l \cdot b \cdot h \]
Substituting the values:
\[ V = 8 \cdot 6 \cdot 3.5 \]

### Step 7: Perform the multiplication.
Calculate \( 8 \cdot 6 = 48 \):
\[ V = 48 \cdot 3.5 \]
Now calculate \( 48 \cdot 3.5 \):
\[ 48 \cdot 3.5 = 168 \, \text{m}^3 \]

### Final Answer:
The volume of the cuboid is \( 168 \, \text{m}^3 \).

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