Cannonballs

Three cannonballs with a diameter of 16 cm landed in the castle courtyard during the battle. The castle blacksmith made balls with a diameter of 10 cm, which fit into the cannons placed on the walls. How many cannonballs did the blacksmith cast?

Correct answer:

n₂ =  12

Step-by-step explanation:

$$\begin{gathered} n_1=3 \\ {D}_1=16\text{cm} \\ {D}_2=10\text{cm} \\ {r}_1=D_1/2=16/2=8\text{cm} \\ {r}_2=D_2/2=10/2=5\text{cm} \\ {V}_1=n_1\cdot \frac{4}{3}\cdot \pi \cdot r_1^3=3\cdot \frac{4}{3}\cdot 3.1416\cdot 8^3\doteq 6433.9818{\text{cm}}^3 \\ {V}_2=\frac{4}{3}\cdot \pi \cdot r_2^3=\frac{4}{3}\cdot 3.1416\cdot 5^3\doteq 523.5988{\text{cm}}^3 \\ {V}_1=n_2\cdot V_2 \\ {n}_2=\lfloor V_1/V_2\rfloor =\lfloor 6433.9818/523.5988\rfloor =12 \end{gathered}$$

Try another example