A solid metal ball of diameter 10 cm is melted and cast into smaller balls of diameter 1 cm. How many such small balls can be made ?
250
500
1000
100
Answer is Wrong!
Answer is Right!
This question was previously asked in
UPSC CISF-AC-EXE – 2021
The large ball has a diameter of 10 cm, so its radius is $R = 10/2 = 5$ cm.
The volume of the large ball is $V_{large} = \frac{4}{3}\pi (5^3) = \frac{4}{3}\pi \times 125$ cm³.
Each smaller ball has a diameter of 1 cm, so its radius is $r = 1/2 = 0.5$ cm.
The volume of a small ball is $V_{small} = \frac{4}{3}\pi (0.5^3) = \frac{4}{3}\pi \times (1/8)$ cm³.
The number of small balls, N, is the total volume of the large ball divided by the volume of a single small ball:
$N = \frac{V_{large}}{V_{small}} = \frac{\frac{4}{3}\pi \times 125}{\frac{4}{3}\pi \times (1/8)} = \frac{125}{1/8} = 125 \times 8$.
$125 \times 8 = 1000$.