Question

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

Answer 1

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

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 * 4a^(2) = 24a^(2) = 4 * 6a^(2)`, which is four times the initial surface area of
  `6a^(2)`.