Physics

A rectangular vessel $$ 1 m \times 0.6 m \times 0.5 m $$ filled with maize grains. Treat the grains spheres of diameter 0.3 cm each.The number of grains in the vessel is the nearest to 


ANSWER

$$ 2 \times 10^7 $$


SOLUTION

Let n number of grains are in the vessel.

So, volume of cuboid vessel is equal to n times volume of spheres. i.e.

$$ 1\times 0.6\times 0.5=n\left( \dfrac{4}{3}\times 3.14\times {{\left( \dfrac{3}{2000} \right)}^{3}} \right) $$

$$ 0.3=n\dfrac{4}{3}\times 3.14\times 3.375\times {{10}^{-9}} $$

$$ 0.3=n\times 14.13\times {{10}^{-9}} $$

$$ n=\dfrac{0.3}{14.13\times {{10}^{-9}}} $$

$$ n=0.021\times {{10}^{9}}\, $$

$$ n=2\times {{10}^{7}}$$

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