Volume of a box is (area of base)$\times$(height). The base is a square with side length $3h$, so what is the area of the base, and then the volume in terms of $h$?

Set your volume expression equal to $1{,}125$. You will get an equation involving $h^3$. After isolating $h^3$, what operation undoes a cube to solve for $h$?

In Desmos, type y = 9x^3 to represent the volume as a function of height $x$ (in inches).

On a new line, type y = 1125. This is the given volume. The intersection point of y = 9x^3 and y = 1125 has an $x$-coordinate equal to the height of the box.

Alternatively, to solve directly, type (1125/9)^(1/3) into Desmos. The output is the value of the height $h$ that satisfies $9h^3 = 1125$.

Let the height of the box be $h$ inches.

The base is a square, and each side of the square is 3 times the height, so the side length of the base is $3h$ inches.

Volume of a rectangular prism $=$ (area of base)$\times$(height).

• Area of the square base is $(3h)^2 = 9h^2$.
• Multiply by the height $h$ to get the volume:

We are told the volume is $1{,}125$ cubic inches, so:

Solve $9h^3 = 1125$:

Now take the cube root of both sides to find $h$.

From $h^3 = 125$, the cube root of $125$ is $5$ because $5^3 = 125$.

So, the height of the box is 5 inches, which corresponds to answer choice C.