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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:

- $\dfrac{2500\pi}{3}$ cubic cm
- $500\pi$ cubic cm
- $2500\pi$ cubic cm
- $\dfrac{5000\pi}{3}$ cubic cm

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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.