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

1. $\dfrac{2500\pi}{3}$ cubic cm
2. $500\pi$ cubic cm
3. $2500\pi$ cubic cm
4. $\dfrac{5000\pi}{3}$ cubic cm

Ans is option (A)

Height of the cylinder $=10\times(2\times5cm)=100cm$ .

$\therefore$  Volume of empty space in the box:  $\pi r^{2}h-(10\times\frac{4}{3}\times \pi \times r^{3})$  cubic cm.

$\Rightarrow$  $(\pi \times 25\times50)-(10\times\frac{4}{3}\times \pi \times 5^{3})=\frac{2500}{3}$ cubic cm.

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