Seven equal cubes each of side 5 cm are joined end-to-end. Find the surface area of the resulting cuboid.

Options

A. 750 sq cm
B. 1500 sq cm
C. 2250 sq cm
D. 700 sq cm

Answer

To find the surface area of the resulting cuboid formed by joining seven equal cubes each of side 5 cm, we can follow these steps:

### Step-by-Step Solution:

1. **Determine the dimensions of the cuboid:**
- Each cube has a side length of 5 cm.
- When 7 cubes are joined end-to-end, the length of the cuboid will be:
\[ \text{Length} = 7 \times 5 \text{ cm} = 35 \text{ cm} \]
- The breadth and height of the cuboid will remain the same as the side of the cube:
\[ \text{Breadth} = 5 \text{ cm}, \quad \text{Height} = 5 \text{ cm} \]

2. **Use the formula for the surface area of a cuboid:**
- The formula for the surface area \( S \) of a cuboid is given by:
\[ S = 2(LB + BH + HL) \]
- Where \( L \) is the length, \( B \) is the breadth, and \( H \) is the height.

3. **Substitute the values into the formula:**
- Substitute \( L = 35 \text{ cm} \), \( B = 5 \text{ cm} \), and \( H = 5 \text{ cm} \) into the formula:
\[ S = 2(35 \times 5 + 5 \times 5 + 5 \times 35) \]

4. **Calculate the individual products:**
- Calculate \( 35 \times 5 = 175 \)
- Calculate \( 5 \times 5 = 25 \)
- Calculate \( 5 \times 35 = 175 \)

5. **Sum the products:**
- Add the results:
\[ 175 + 25 + 175 = 375 \]

6. **Multiply by 2 to find the total surface area:**
- Finally, multiply by 2:
\[ S = 2 \times 375 = 750 \text{ cm}^2 \]

### Final Answer:
The surface area of the resulting cuboid is \( 750 \text{ cm}^2 \).

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