What is the effect that doubling the side length on a cube has on its surface area?

ok so the surface area of a cube

it has 6 square sides
so
SA=6side^2

if each side was doubled
SA=6(2side)^2
SA=6*4(side)^2
SA=24side^2

compared to original
SA=6side^2
and
SA=24side^2

it increases by 4 times

Answer Link

TheBlueFox TheBlueFox · Answer 2 · 2019-10-14T19:32:24+02:00

Answer: The new cube will become 4 times larger.

Step-by-step explanation: To determine what happens to the surface area of a cube if we double the length of a side, let's start by choosing a length for the side of our cube.

For example, let's say our cube has a side length of 2. Next, to find its surface area we simply add the areas of the faces of the cube. Since each face of the cube is a square with a side length of 2, the area of each face is 2 multiplied by 2 which is 4. Since there are 6 square faces in a cube, we multiply 6 by 4 to get 24 which represents the surface area of the cube.

Now, let's double the length of a side so each side will have a side length of 4. Since each face of the cube is a square with a side length of 4, the area of each face is 4 multiplied by 4 which is 16. Since there are 6 square faces in a cube, we multiply 6 by 16 to get 96 which represents the surface area of our new cube.

Finally, notice that our new cub has a surface area that is 4 times the surface area of the old cube.

Therefore, if we double the length of a side, we can see that the surface area becomes 4 times larger.

I'll attach an image to show the cubes and the surface area.