Question 5

Explanation

Volume Analysis

The remaining water volume is the difference between the cylinder volume (initial water) and the total volume of the balls inserted.

Substitute $r_1 = 16 \text{ cm}$ and $t = 20 \text{ cm}$ for the cylinder, and $r_2 = 6 \text{ cm}$ for the ball.

Simplify the equation by dividing both sides by 32:

Since $n$ represents the number of balls, $n$ must be an integer. Furthermore, the total volume of the balls cannot exceed the capacity that allows for $64\pi$ of remaining water (if $n=18$, the remaining water would be negative, which is impossible).

Therefore, the number of balls inserted is $17$ balls.