Question

a formula for determining the mean free path for sound, or the average distance a wave travels in a room, is determined by dividing four times the volume by the surface area of the space. the formula for volume (v) of a cube is expressed as the as the product of a side cubed. the surface area (s) of a cube is expressed as six times the product of a side squared. see the following formula. $\frac{4v}{s}$ or $(4\times v)div s$ thus, the formula could be rewritten as follows, where lower case s equals a side of a cube. $\frac{4(s^{3})}{6(s^{2})}$ solve for a room that is a cube with a side of 4 meters. (you do not need to include the units. only enter the number value for an answer. round to the nearest hundredth if necessary.)

Explanation:

Step1: Substitute s = 4 into the formula

Substitute \(s = 4\) into \(\frac{4(s^{3})}{6(s^{2})}\).

Step2: Simplify the formula

First, simplify \(\frac{4(s^{3})}{6(s^{2})}\) to \(\frac{4s}{6}\) (using the rule \(\frac{a^{m}}{a^{n}}=a^{m - n}\), here \(m = 3\), \(n=2\)). Then when \(s = 4\), we have \(\frac{4\times4}{6}=\frac{16}{6}\).

Step3: Calculate the result

\(\frac{16}{6}\approx2.67\) (rounded to the nearest hundred - th).

Answer:

2.67