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

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?

1 Answer

Impact of this question

3853 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-05-05T02:43:26

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

This is because we find the area of one side $s^{2}$ $s^2$ , 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 $1.5 s$ $1.5s$ Think about it. We have $1 s$ $1s$ originally, then increasing by 50% of 1 is $0.5$ $0.5$ , so we have $1.5 s$ $1.5s$

We just plug this in for the surface area formula

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

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

$\frac{13.5 s^{2}}{6 s^{2}}$ $(13.5s^2) / (6s^2)$

We simplify this, and we get $2.25$ $2.25$

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

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

I chose $s = 8$ $s=8$ , 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.

Science

Math

Humanities

... and beyond

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

1 Answer

Related questions

Impact of this question