Question

the surface area of this cube is 384 square centimeters. what is the volume? cubic centimeters submit

Explanation:

Step1: Find the side length of the cube

The surface area formula of a cube is \(S = 6a^{2}\), where \(S\) is the surface area and \(a\) is the side - length. Given \(S=384\) \(cm^{2}\), we have \(6a^{2}=384\). Then \(a^{2}=\frac{384}{6} = 64\), and \(a=\sqrt{64}=8\) \(cm\).

Step2: Calculate the volume of the cube

The volume formula of a cube is \(V=a^{3}\). Substitute \(a = 8\) into the formula, we get \(V=8^{3}=8\times8\times8 = 512\) \(cm^{3}\).

Answer:

\(512\)