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. 126
B. 168
C. 224
D. 112

Answer

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

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

### Step 2: Substitute the known values into the TSA formula.
Given:
- Total surface area \( TSA = 194 \, m^2 \)
- Length \( l = 8 \, m \)
- Breadth \( b = 6 \, m \)

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

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

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

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

### Step 6: Calculate the volume of the cuboid.
The volume \( V \) of a cuboid is given by the formula:
\[ V = l \cdot b \cdot h \]
Substituting the values:
\[ V = 8 \cdot 6 \cdot 3.5 \]
Calculating \( 8 \cdot 6 \):
\[ 8 \cdot 6 = 48 \]
Now, calculate the volume:
\[ V = 48 \cdot 3.5 = 168 \, m^3 \]

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

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