The area of the cardboard needed to make a closed box of size 10 cm `xx` 15 cm `xx` 8 cm will be:

Options

A. `700 cm^(2)`
B. `350 cm^(2)`
C. `1000 cm^(2)`
D. `1390 cm^(2)`

Answer

To find the area of cardboard needed to make a closed box with dimensions 10 cm, 15 cm, and 8 cm, we need to calculate the total surface area (TSA) of the box. The formula for the total surface area of a cuboid is given by:

\[ \text{Total Surface Area (TSA)} = 2 \times (l \times b + b \times h + l \times h) \]

Where:
- \( l \) = length
- \( b \) = breadth
- \( h \) = height

### Step 1: Identify the dimensions of the box
- Length (\( l \)) = 10 cm
- Breadth (\( b \)) = 15 cm
- Height (\( h \)) = 8 cm

### Step 2: Substitute the dimensions into the TSA formula
Now, substituting the values into the formula:

\[ TSA = 2 \times (10 \times 15 + 15 \times 8 + 10 \times 8) \]

### Step 3: Calculate the area of each face
- Calculate \( l \times b \):
\[ 10 \times 15 = 150 \, \text{cm}^2 \]

- Calculate \( b \times h \):
\[ 15 \times 8 = 120 \, \text{cm}^2 \]

- Calculate \( l \times h \):
\[ 10 \times 8 = 80 \, \text{cm}^2 \]

### Step 4: Sum the areas of the three pairs of faces
Now, add these areas together:
\[ 150 + 120 + 80 = 350 \, \text{cm}^2 \]

### Step 5: Multiply by 2 to get the total surface area
Now, multiply the sum by 2:
\[ TSA = 2 \times 350 = 700 \, \text{cm}^2 \]

### Conclusion
The area of cardboard needed to make the closed box is:
\[ \boxed{700 \, \text{cm}^2} \]