Question

the surface area of this cube is 2,166 square inches. what is the value of z?
z = \boxed{} inches

Explanation:

Step1: Recall cube surface area formula

A cube has 6 equal square faces. The surface area \( S \) of a cube with side length \( z \) is given by the formula \( S = 6z^2 \).

Step2: Substitute given surface area

We know the surface area \( S = 2166 \) square inches. So we set up the equation:
\( 6z^2 = 2166 \)

Step3: Solve for \( z^2 \)

Divide both sides of the equation by 6:
\( z^2=\frac{2166}{6} = 361 \)

Step4: Solve for \( z \)

Take the square root of both sides. Since \( z \) represents a length (positive), we take the positive square root:
\( z=\sqrt{361}=19 \)

Answer:

\( z = \boxed{19} \) inches