Question

A cylindrical rod whose height is 8 times of its radius is melted and recast into spherical balls of same radius. The number of balls will be
A. 4
B. 3
C. 6
D. 8

Answer 1

Answer: C) 6

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Step-by-step explanation:

Answer 2

The number of balls will be 6

Solution:

Given that,

A cylindrical rod whose height is 8 times of its radius

h = 8r

A cylindrical rod whose height is 8 times of its radius is melted and recast into spherical balls of same radius

Let the number of balls be n

Therefore,

$\text{ Volume of cylinder } = n \times \text{ Volume of sphere }$

$\pi r^2 h = n \times \frac{4}{3} \pi r^3\\\\\pi r^2 \times 8r = n \times \frac{4}{3} \pi r^3\\\\8 = n \times \frac{4}{3}\\\\n = 2 \times 3\\\\n = 6$

Thus number of balls will be 6

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