Theoretically 35321

Calculate how many soccer balls (the volume of one is 7,200 cm³) theoretically fit into a room with dimensions of 8x5x3 m. Neglect the gaps between the balls.

Correct answer:

n =  8727

Step-by-step explanation:

$$\begin{gathered} V_1=7200{\text{cm}}^3\to {\text{m}}^3=7200:1000000{\text{m}}^3=0.0072{\text{m}}^3 \\ a=8\text{m} \\ b=5\text{m} \\ c=3\text{m} \\ {V}_2=a\cdot b\cdot c=8\cdot 5\cdot 3=120{\text{m}}^3 \\ {n}_1=V_2/V_1=120/0.0072=\frac{50000}{3}=16666\frac{2}{3}\doteq 16666.6667 \\ {V}_1=\frac{4}{3}\pi r^3 \\ r=\sqrt[3]{3\cdot V_1/(4\pi )}=\sqrt[3]{3\cdot 0.0072/(4\cdot 3.1416)}\doteq 0.1198\text{m} \\ {V}_3=(2\cdot r{)}^3=(2\cdot 0.1198{)}^3\doteq 0.0138{\text{m}}^3 \\ {n}_2=V_2/V_3=120/0.0138\doteq 8726.6463 \\ {n}_2<n<n_1 \\ n=n_2=8726.6463=8727 \end{gathered}$$

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