Question

what is the length of the sides of a cube with surface area 54m²? a) 3 m b) 9 m c) 7.3 m d) 3.8 m

Explanation:

Step1: Recall surface - area formula

The surface - area formula of a cube is $S = 6s^{2}$, where $S$ is the surface area and $s$ is the side - length of the cube.

Step2: Substitute the given surface area

We are given that $S = 54m^{2}$, so $54=6s^{2}$.

Step3: Solve for $s^{2}$

Divide both sides of the equation by 6: $\frac{54}{6}=s^{2}$, which simplifies to $s^{2}=9$.

Step4: Solve for $s$

Take the square root of both sides. Since $s$ represents a length, we take the positive square root: $s = 3m$.

Answer:

a) 3 m