Question

For any cube with edges of length \(s,\) what is the ratio of the surface area to the volume?

Short answer

Answer: The ratio of the surface area to the volume of a cube with edge length s is 6/s.

Step-by-step solution

Calculate the surface area of the cube

The surface area of a cube can be calculated using the formula \(A = 6s^2\) where \(A\) is the surface area and \(s\) is the length of the edges. In this case, the surface area is \(A = 6s^2\).

Calculate the volume of the cube

The volume of a cube can be calculated using the formula \(V = s^3\) where \(V\) is the volume and \(s\) is the length of the edges. In this case, the volume is \(V = s^3\).

Find the ratio of surface area to volume

Now, we can find the ratio of the surface area to the volume by dividing the surface area by the volume: \(\frac{A}{V} = \frac{6s^2}{s^3} = \frac{6}{s}\) So, the ratio of the surface area to the volume for any cube with edges of length \(s\) is \(\frac{6}{s}\).