Question

The difference between the total surface area and lateral surface area of a cube
of side 4cm is --------.

Answer 1

Step-by-step explanation:

The difference between the total surface area of a cube of side 4 cm and its lateral surface area is. 24 sq cm.

Answer 2

Given:

The side of the cube=4cm

To find:

The difference between the total surface area and lateral surface area of the cube

Solution:

The difference between the total surface area and lateral surface area of the cube is 32cm².

We can find the difference by following the given steps-

We know that the total surface area of a cube includes the area of all its surfaces while the lateral surface area includes the area of just four sides.

Let the side of the cube be s.

The area of a square is s².

Since a cube has 6 faces, the total surface of the cube=6×s²=6s²

Similarly, the lateral surface area of the cube=4×s²=4s²

The length of the side of the cube is 4cm.

So, s=4cm.

The total surface area of the cube=6×4²

=6×16

=96cm²

Now, the lateral surface area of the cube=4×4²

=4³=64cm²

We will subtract the total and lateral surface areas to obtain the difference.

The difference between the total and lateral surface area of the cube=6s²-4s²

=96-64

=32cm²

Therefore, the difference between the total surface area and lateral surface area of the cube is 32cm².