Question

Each edge of a cube is increased by 50%. How do you find the percentage of increase in the surface area of the cube?

Answer 1

Remember that the formula for the surface area of a cube is `6s^2`

This is because we find the area of one side `s^2`, then multiply it by the number of sides a cube has, which is 6.

So, if we increase the edge length of a cube, instead of s, we are going to have `1.5s` Think about it. We have `1s` originally, then increasing by 50% of 1 is `0.5`, so we have `1.5s`

We just plug this in for the surface area formula

`6*(1.5s)^2` = `13.5s^2`

We want to calculate the percentage of increase, so we put this new surface area over the original surface area.

`(13.5s^2) / (6s^2)`

We simplify this, and we get `2.25`

This is in decimal format, we move over the decimal to get `225%`

We can choose a random side length to check our answer:

I chose `s=8`, which gave 384 as the original surface area, 864 as the surface area of 12 (8 with a 50% increase)

We multiply 384 by 2.25 and we get 864.