Question 11

A cylindrical box of radius 5 cm contains 10 solid spherical balls, each of radius 5 cm. If the top most ball touches the upper cover of the box, then the volume of empty space in the box is :

Solution

It is given, cylindrical box of radius 5 cm contains 10 solid spherical balls, each of radius 5 cm.

So, height of the cylinder = $$10\times\ 2r=10\times\ 2\times\ 5=100$$ cm.

So, volume of cylinder = $$\pi\ r^2h=\pi\ \times\ 5^2\times\ 100=2500\pi\ $$ $$cm^3$$

Now, volume of one sphere = $$\dfrac{4}{3}\pi\ r^3=\dfrac{4}{3}\times\pi\ \times\ 5^3=\dfrac{500}{3}\pi\ $$ $$cm^3$$

So, volume of 10 spheres = $$\dfrac{500}{3}\times\ 10\ \pi\ =\dfrac{5000}{3}\pi\ $$ $$cm^3$$

So, volume of empty space in the box = $$2500\pi\ -\dfrac{5000}{3}\pi=\dfrac{2500}{3}\ \pi$$ $$cm^3$$

So, the correct answer is option A.

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