The volume of a cuboid is 320 cubic cm. Find its total surface area if its length and breadth are 10 cm and 8 cm respectively ?

Options

A. a) 608 sq. cm
B. b) 304 sq. cm
C. c) 152 sq. cm
D. d) 456 sq. cm

Answer

To solve the problem step by step, we need to find the height of the cuboid first and then calculate its total surface area.

### Step 1: Write down the formula for the volume of a cuboid.
The volume \( V \) of a cuboid is given by the formula:
\[ V = l \times b \times h \]
where \( l \) is the length, \( b \) is the breadth, and \( h \) is the height.

### Step 2: Substitute the known values into the volume formula.
We know:
- Volume \( V = 320 \, \text{cm}^3 \)
- Length \( l = 10 \, \text{cm} \)
- Breadth \( b = 8 \, \text{cm} \)

Substituting these values into the volume formula:
\[ 320 = 10 \times 8 \times h \]

### Step 3: Simplify the equation to find the height \( h \).
Calculating \( 10 \times 8 \):
\[ 10 \times 8 = 80 \]
So, we can rewrite the equation as:
\[ 320 = 80 \times h \]

### Step 4: Solve for \( h \).
To find \( h \), divide both sides by 80:
\[ h = \frac{320}{80} = 4 \, \text{cm} \]

### Step 5: Write down the formula for the total surface area (TSA) of a cuboid.
The total surface area \( A \) of a cuboid is given by the formula:
\[ A = 2(lb + bh + hl) \]

### Step 6: Substitute the values of \( l \), \( b \), and \( h \) into the TSA formula.
Substituting \( l = 10 \, \text{cm} \), \( b = 8 \, \text{cm} \), and \( h = 4 \, \text{cm} \):
\[ A = 2(10 \times 8 + 8 \times 4 + 4 \times 10) \]

### Step 7: Calculate each term inside the parentheses.
Calculating each term:
- \( 10 \times 8 = 80 \)
- \( 8 \times 4 = 32 \)
- \( 4 \times 10 = 40 \)

Now, add these values together:
\[ 80 + 32 + 40 = 152 \]

### Step 8: Multiply by 2 to find the total surface area.
Now, multiply by 2:
\[ A = 2 \times 152 = 304 \, \text{cm}^2 \]

### Final Answer:
The total surface area of the cuboid is:
\[ \text{Total Surface Area} = 304 \, \text{cm}^2 \]

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