Set your surface area formula equal to 150 and solve for $s$. What equation do you get, and how can you isolate $s$?

Once you know the side length $s$, recall the formula for the volume of a cube. How do you use $s$ to compute the volume?

In the Desmos expression line, type 150/6 and note the value shown. This represents $s^2$ from the equation $6s^2 = 150$.

In a new line, type sqrt(150/6) to compute the side length $s$ of the cube. This gives the positive square root of $s^2$.

In another line, type (sqrt(150/6))^3 to calculate the cube’s volume. The value Desmos outputs here is the volume in cubic inches.

For a cube with side length $s$:

• Each face has area $s^2$.
• A cube has 6 congruent square faces.

So the total surface area $A$ is:

We are told the total surface area is 150 square inches, so:

Solve the equation $6s^2 = 150$ for $s$.

First divide both sides by 6:

Now take the positive square root (side length must be positive):

So the side length of the cube is 5 inches.

The volume $V$ of a cube with side length $s$ is:

Substitute $s = 5$:

So the volume of the cube is 125 cubic inches, which corresponds to answer choice C.