| A solid sphere of radius 5 cm is melted and then cast into small spherical balls each of diameter 10 mm. Find the number of balls made. |
A) 50
B) 1000
C) 100
D) 500
Correct Answer: B
Solution :
(b)| Radius of the sphere \[=5\,\,cm\] |
| Volume of the sphere \[=\frac{4}{3}\times \pi \times 5\times 5\times 5\] |
| Radius of the small sphere \[=\frac{1}{2}cm\] |
| Volume of each small sphere\[=\frac{4}{3}\times \pi \times \frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}\] |
| \[\therefore \]Number of balls made \[=\frac{\frac{4}{3}\times \pi \times 5\times 5\times 5}{\frac{4}{3}\times \pi \times \frac{1}{2}\times \frac{1}{2}\times \frac{1}{2}}=1000\] |
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