Answer:
32 solid balls are formed.
Step-by-step explanation:
Let suppose that volume of the cone is equal to the total volume of balls, of which we derive the following formula:
[tex]\frac{1}{3}\cdot \pi\cdot R^{2}\cdot h = \frac{1}{6}\cdot \pi \cdot n \cdot D^{3}[/tex] (1)
Where:
[tex]R[/tex] - Radius of the base of cone, measured in centimeters.
[tex]h[/tex] - Height of cone, measured in centimeters.
[tex]D[/tex] - Diameter of sphere, measured in centimeters.
[tex]n[/tex] - Number of balls, no unit.
Then, we clear the number of balls:
[tex]2\cdot R^{2}\cdot h = n\cdot D^{3}[/tex]
[tex]n = \frac{2\cdot R^{2}\cdot h}{D^{3}}[/tex]
If we know that [tex]R = 12\,cm[/tex], [tex]h = 24\,cm[/tex] and [tex]D = 6\,cm[/tex], then the number of balls is:
[tex]n = \frac{2\cdot (12\,cm)^{2}\cdot (24\,cm)}{(6\,cm)^{3}}[/tex]
[tex]n = 32[/tex]
32 solid balls are formed.
