Question

persevere find the volume of a cube that has a total surface area of 54 square millimeters. mm³ need help with this question? get a hint show answer

Explanation:

Step1: Recall surface - area formula

The surface - area formula of a cube is $S = 6s^{2}$, where $s$ is the side - length of the cube. Given $S = 54$ square millimeters, we have the equation $6s^{2}=54$.

Step2: Solve for side - length $s$

Divide both sides of the equation $6s^{2}=54$ by 6: $s^{2}=\frac{54}{6}=9$. Then take the square root of both sides. Since $s>0$ (as it represents a length), $s = 3$ mm.

Step3: Recall volume formula

The volume formula of a cube is $V=s^{3}$.

Step4: Calculate volume

Substitute $s = 3$ mm into the volume formula: $V=3^{3}=27$ $mm^{3}$.

Answer:

27