Question

the surface area of this cube is 2,400 square millimeters. what is the value of c?
c = millimeters
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Explanation:

Step1: Recall the surface area formula for a cube

A cube has 6 identical square faces. The area of one square face is \( c^2 \) (where \( c \) is the side length of the cube), so the surface area \( S \) of a cube is given by the formula \( S = 6c^2 \).

Step2: Substitute the given surface area into the formula

We know that the surface area \( S = 2400 \) square millimeters. So we set up the equation:
\[
6c^2 = 2400
\]

Step3: Solve for \( c^2 \)

Divide both sides of the equation by 6:
\[
c^2=\frac{2400}{6} = 400
\]

Step4: Solve for \( c \)

Take the square root of both sides. Since \( c \) represents a length, we take the positive square root:
\[
c=\sqrt{400}=20
\]

Answer:

20