Question

Assertion: Two cubes of side 2 cm are joined together to form a cuboid the surface area of a cuboid is 40 cm².

Reason: The surface area of a cuboid is the sum of the surface areas of the two cubes.

विकल्प

• Both A and R are true and R is the correct reason for A.

• Both A and R are true but R is the incorrect reason for A.

• A is true but R is false.

• A is false but R is true.

Answer 1

A is true but R is false.

Explanation:

Step 1: Volume and structure

When two cubes (side = 2 cm) are joined face to face, we get a cuboid with:

Length = 2 + 2 = 4 cm

Breadth  = 2 cm

Height = 2 cm

Now compute the surface area of the cuboid:

Surface Area = 2(lb + bh + hl) = 2(4 × 2 + 2 × 2 + 2 × 4)

= 2(8 + 4 + 8) = 2(20) = 40 cm²

So, the Assertion is TRUE.

When you join two cubes, the joined face becomes internal and is no longer part of the external surface. So:

New surface area < Surface area of two individual cubes

Each cube’s surface area is:

6a² = 6(2²) = 24 cm² ⇒ 2 × 24 = 48 cm²

But the resulting cuboid has only 40 cm², not 48. So:

Reason is FALSE.