Centimeter 7821

What should a sweet tooth choose if he wants more chocolate: a package containing 200 pieces of solid chocolate balls with a diameter of 1 centimeter or a hollow ball with an outer diameter of 10 cm made of 5 mm thick chocolate?

Correct answer:

x =  2

Step-by-step explanation:

$$\begin{gathered} D_1=1\text{cm} \\ {r}_1=D_1/2=1/2=\frac{1}{2}=0.5\text{cm} \\ {V}_1=200\cdot \frac{4}{3}\cdot \pi \cdot r_1^3=200\cdot \frac{4}{3}\cdot 3.1416\cdot 0.5^3\doteq 104.7198{\text{cm}}^3 \\ {D}_2=10\text{cm} \\ h=5\text{mm}\to \text{cm}=5:10\text{cm}=0.5\text{cm} \\ {r}_2=D_2/2=10/2=5\text{cm} \\ {r}_3=r_2-h=5-\frac{1}{2}=\frac{5\cdot 2}{2}-\frac{1}{2}=\frac{10}{2}-\frac{1}{2}=\frac{10-1}{2}=\frac{9}{2}=4.5\text{cm} \\ {V}_2=\frac{4}{3}\cdot \pi \cdot r_2^3-\frac{4}{3}\cdot \pi \cdot r_3^3=\frac{4}{3}\cdot 3.1416\cdot 5^3-\frac{4}{3}\cdot 3.1416\cdot 4.5^3\doteq 141.8953{\text{cm}}^3 \\ {V}_2>V_1 \\ x=2 \end{gathered}$$

Try another example