Question

If the length of each edge of the cube is doubled, the surface area will increase 2 times.True or false

Answer 1

Answer:

False. The surface area of the cube will increase to four times its initial value.

Step-by-step explanation:

Consider a cube with edge of lengths $a$. What will be its surface area?

Each face of a cube is a square. The lengths of sides of the square are also $a$.

The area of each square will be the square of its sides: $a \cdot a = a^{2}$.

It takes six such squares to make a cube. The sum of the area of the sube $6a^{2}$ will also be the surface area of the cube.

In case the length of each side of the cube is doubled to $2a$.

• The area of each face will become $(2a)^{2} = 4a^{2}$.
• The sum of the area of the six sides will become $6 \times 4a^{2} = 24a^{2} = 4 \times 6a^{2}$, which is four times the initial surface area of $6a^{2}$.