Decorations 81510

The glass Christmas decorations have the shape of a ball with a diameter of 8 cm. In a small family business, they produce 50,000 pieces a year. The entire surface of these balls is covered with glitter. 400 g of glitter is needed to cover an area of 1 m². How many kilograms of glitter are needed to cover all the balls made?

Correct answer:

m =  402.1239 kg

Step-by-step explanation:

$$\begin{gathered} d=8\text{cm}\to \text{m}=8:100\text{m}=0.08\text{m} \\ n=50000 \\ r=d/2=0.08/2=\frac{1}{25}=0.04\text{m} \\ {S}_1=4\pi \cdot r^2=4\cdot 3.1416\cdot 0.04^2\doteq 0.0201{\text{m}}^2 \\ {S}_2=n\cdot S_1=50000\cdot 0.0201\doteq 1005.3096{\text{m}}^2 \\ {m}_1=400\text{g}\to \text{kg}=400:1000\text{kg}=0.4\text{kg} \\ m=S_2\cdot m_1=1005.3096\cdot 0.4=402.1239\text{kg} \end{gathered}$$

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