Question

The surface area of a cube is `216 cm^2`. What are the dimensions of this cube?

Answer 1

The length, height, and width of the cube is 6 cm.

Explanation:

Surface area is defined as all the area on the outside of an object, like the cube in this case. Since a cube has 6 faces, we know that for the first part of our equation, we have a 6. The 6 will be multiplying the area of the faces, so now we just need to find the formula for the area. Since the length and widths are equal, we can say that area is `x*x` or `x^2`. When we combine that with the 6, we get an equation of `6x^2`.

Now we just need to set up the equation. We say that `216 = 6x^2` and we start off by dividing by 6 on both sides. That yields an answer of `36 = x^2`. Our final step is to square root both sides to get an answer of `6 = x`. Since x was our width/length, we can say that all the dimensions are 6 cm.

Answer 2

See a solution process below:

Explanation:

The formula for the surface area of a cube is:

`S = 6a^2`

Where:

`S` is the Surface Area: `216"cm"^2` for this problem.

`a` is the length of each side of the cube: What we are solving for in this problem.

Substituting and solving for `a` gives:

`216"cm"^2 = 6a^2`

First, divide each side of the equation by `color(red)(6)` to isolate the `a` term while keeping the equation balanced:

`(216"cm"^2)/color(red)(6) = (6a^2)/color(red)(6)`

`36"cm"^2 = (color(red)(cancel(color(black)(6)))a^2)/cancel(color(red)(6))`

`36"cm"^2 = a^2`

Now we can take the square root of each side of the equation to solve for `a` while keeping the equation balanced. We can ignore the negative square root of the number of the left side of the equation because we are looking for a positive distance for the length of a side:

`sqrt(36"cm"^2) = sqrt(a^2)`

`6"cm" = a`

`a = 6"cm"`

The dimensions of the cube is:

`6"cm" xx 6"cm" xx 6"cm"`