Question

Two cubes of edge 3 cm are joined together to form a cuboid. Its surface area is ______.

Options

• 90 cm²

• 120 cm²

• 150 cm²

• 144 cm²

Answer 1

Two cubes of edge 3 cm are joined together to form a cuboid. Its surface area is 90 cm².

Explanation:

Step 1: Find the volume of one cube

The volume V of a cube with edge length s is:

V = s³

For a cube with edge length 3 cm:

V = 3³ = 27 cm³

Thus, the volume of one cube is 27 cm³.

Since there are two cubes, the total volume of the cuboid is:

Total volume = 2 × 27 = 54 cm³

Step 2: Find the dimensions of the cuboid

When the two cubes are joined together, the resulting cuboid has one of its dimensions equal to the sum of the edges of the cubes. The edge length of each cube is 3 cm, so the new dimension of the cuboid is:

Length = 3 + 3 = 6 cm

The other two dimensions of the cuboid remain the same as the edge of the cube:

Width = 3 cm,

Height = 3 cm

Thus, the dimensions of the cuboid are 6 cm × 3 cm × 3 cm.

Step 3: Find the surface area of the cuboid

The surface area A of a cuboid is given by the formula:

A = 2(lw + lh + wh)

Where l is the length, w is the width and h is the height. 

Substituting the values for l = 6 cm, w = 3 cm and h = 3 cm:

A = 2(6 × 3 + 6 × 3 + 3 × 3)

A = 2(18 + 18 + 9) = 2(45) = 90 cm²