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

$\frac{4(s^{3})}{6(s^{2})}=\frac{4\times4^{3}}{6\times4^{2}}$

Step2: Simplify the exponents

$4^{3}=4\times4\times4 = 64$, $4^{2}=4\times4 = 16$. So we have $\frac{4\times64}{6\times16}$

Step3: Calculate the numerator and denominator

$4\times64 = 256$, $6\times16=96$. So the fraction is $\frac{256}{96}$

Step4: Simplify the fraction

$\frac{256}{96}=\frac{8}{3}\approx2.67$

Answer:

2.67