How many solid cylinders of radius 10 cm and height 6 cm can be m… - Vidyadip

Question

How many solid cylinders of radius 10 cm and height 6 cm can be made by melting a solid sphere of radius 30 cm?

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Answer

Volume of sphere = $\frac{4}{3} \pi R^{3} = \frac{4}{3} \pi (30)^{3}$
Volume of one cylinder = $\pi r^{2} h = \pi (10)^{2} (6)$
Number of cylinders $n = \frac{\text{Volume of sphere}}{\text{Volume of cylinder}}$
$n = \frac{\frac{4}{3} \pi \times 30 \times 30 \times 30}{\pi \times 10 \times 10 \times 6}$
$n = \frac{4 \times 10 \times 30 \times 30}{100 \times 6} = \frac{36000}{600} = 60$

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