Question

10 fill in the blank 1 point
a sports equipment company packs 15 balls of varying sizes in containers. the function $f(x) = 10\left(\frac{4}{3}\pi x^{3}\
ight)$ represents the capacity required to hold 15 balls with radius x inches. the table below shows several values of x and f(x) rounded to the nearest hundredths.

x	f(x)
4	2680.83
6	9047.79
8	21446.61

the average rate of change in the capacity of a container holding 2-inch ball to a container holding 8-inch ball is approximately type your answer... cubic inches per inch of increase in the radius of the ball.

Explanation:

Step1: Recall average rate of change formula

$\text{Average Rate of Change} = \frac{f(x_2)-f(x_1)}{x_2-x_1}$

Step2: Identify values from the table

$x_1=2, f(x_1)=335.10; x_2=8, f(x_2)=21346.61$

Step3: Substitute values into formula

$\frac{21346.61 - 335.10}{8 - 2} = \frac{21011.51}{6}$

Step4: Calculate the final result

$\frac{21011.51}{6} \approx 3001.92$

Answer:

3001.92