Question

If each edge of a cube is doubled, how many times will its surface area increase?

Answer 1

Let the side of cube = l

Then surface area of the old cube = 6l²             ...(i)

If each edge of the cube is doubled, then side = 2 × l

Then surface area of the new cube = 6(2l)² = 6 × 4l²

= 4 × 6l²   ...(ii)

From equations (i) and (ii),

Surface area of new cube = 4 × surface area of old cube

Therefore, in this situation, the surface area of the cube will increase four times.