Question

A solid is made by joining corresponding faces of two cubes each of side 10 cm. The surface area of the resulting cuboid will be:

• A. $1200\ \text{cm}^2$
• B. $1800\ \text{cm}^2$
• C. $2000\ \text{cm}^2$
• D. $1000\ \text{cm}^2$

Hint:

When combining solids, remember to subtract the area of the hidden/common faces from the total surface area.

Answer 1

The Correct Option is B

Step 1: Dimensions of the new solid
Each cube has side $= 10$ cm. By joining two cubes face-to-face, we get a cuboid of dimensions:
\[ \text{Length} = 20\ \text{cm}, \text{Breadth} = 10\ \text{cm}, \text{Height} = 10\ \text{cm} \]

Step 2: Formula for surface area of a cuboid
\[ \text{SA} = 2(lb + bh + hl) \]

Step 3: Substitute values
\[ SA = 2(20 \times 10 + 10 \times 10 + 10 \times 20) \] \[ = 2(200 + 100 + 200) = 2 \times 500 = 1000\ \text{cm}^2 \]

Step 4: Re-check carefully
Wait! When two cubes are joined, the common face (area $= 10 \times 10 = 100$) is hidden on both cubes. So, from total surface area of two cubes:
Each cube SA $= 6a^2 = 6 \times 100 = 600$. For two cubes: $1200$. Subtract $2 \times 100 = 200$ (common faces) = $1000$.
But option (D) $1000$ is present. So, correct is (D), not (B).
\[ \boxed{\text{Surface Area} = 1000\ \text{cm}^2} \]