### Instruction: When each edge of a cube is increased by $50\%$, by what percent is the surface area of the cube increased?### Response: So the surface area of the original cube is 6 times the area of each face.
And each face is a square, so its area is the length of each edge squared.
Let's call the length of each edge x. So the surface area of the original cube is 6*$x^2$.
And if we increase the length of each edge by 50%, we get 1.5*x.
So the area of each face is $(1.5*x)^2$ which is $2.25*x^2$.
So the surface area of the new cube is 6*$2.25*x^2$ which is $13.5*x^2$.
And if we divide that by the original surface area, we get $13.5*x^2$/$6*x^2$ which is 2.25.