benchmark 1 spiral\nthe volume of a cube is ( v(s)=s^{3} ), where ( s ) is the side length (in ( mathrm{cm}…

benchmark 1 spiral\nthe volume of a cube is ( v(s)=s^{3} ), where ( s ) is the side length (in ( mathrm{cm} )).\nfind the average rate of change of volume as ( s ) increases from ( 2 mathrm{~cm} ) to ( 5 mathrm{~cm} ).\n39\n50\n3\n117

benchmark 1 spiral\nthe volume of a cube is ( v(s)=s^{3} ), where ( s ) is the side length (in ( mathrm{cm} )).\nfind the average rate of change of volume as ( s ) increases from ( 2 mathrm{~cm} ) to ( 5 mathrm{~cm} ).\n39\n50\n3\n117

Answer

Explanation:

Step1: Recall the formula for average rate of change

The formula for the average rate of change of a function (y = f(x)) from (x=a) to (x = b) is (\frac{f(b)-f(a)}{b - a}). Here, (f(s)=s^{3}), (a = 2), and (b = 5).

Step2: Calculate (f(5)) and (f(2))

  • For (s = 5), (f(5)=5^{3}=125).
  • For (s = 2), (f(2)=2^{3}=8).

Step3: Substitute into the average - rate - of - change formula

(\frac{f(5)-f(2)}{5 - 2}=\frac{125 - 8}{3}). First, calculate the numerator: (125-8 = 117). Then, divide by the denominator: (\frac{117}{3}=39).

Answer:

39