Question

the surface area of this cube is 1,536 square centimeters. what is the value of d?
d = \square centimeters

Explanation:

Step1: Recall the formula for the surface area of a cube

A cube has 6 faces, and each face is a square with side length \( d \). The area of one square face is \( d \times d = d^2 \). So the surface area \( S \) of a cube is given by the formula \( S = 6d^2 \).

Step2: Substitute the given surface area into the formula

We know that the surface area \( S = 1536 \) square centimeters. So we set up the equation:
\[
6d^2 = 1536
\]

Step3: Solve for \( d^2 \)

Divide both sides of the equation by 6:
\[
d^2 = \frac{1536}{6} = 256
\]

Step4: Solve for \( d \)

Take the square root of both sides. Since \( d \) represents a length, we take the positive square root:
\[
d = \sqrt{256} = 16
\]

Answer:

16