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

May 5, 2016

Remember that the formula for the surface area of a cube is $6 {s}^{2}$

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 $1.5 s$ Think about it. We have $1 s$ originally, then increasing by 50% of 1 is $0.5$, so we have $1.5 s$

We just plug this in for the surface area formula

$6 \cdot {\left(1.5 s\right)}^{2}$ = $13.5 {s}^{2}$

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

$\frac{13.5 {s}^{2}}{6 {s}^{2}}$

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.