Question

A cylindrical metal rod, whose height is 8 times its radius, is melted and cast into spherical balls, each of half the radius
of the cylinder. The number of balls are:​

Answer 1

Solution ✌️

Now let the base radius of the rod(cylindrical)

=r

now .. height(h) of the rod=8r

now..

it's volume=πr²h=π(r)²(8r)=8πr³

now..

radius of the spherical ball(R)=r/2

now.. volume of the spherical ball

=4πR³/3

=4πr³/24

=πr³/6

now ..number of spherical balls that can be

made from cylindrical rod

$= \frac{8\pi \:r {}^{3} }{ \frac{\pi \: r {}^{3} }{6} } \\ = 48 \: pcs$

Hope this helps you

Answer 2

Let the number of balls = n.

Given, Height is 8 times its radius => h = 8 * r

∴ Volume of cylinder = n * Volume of Sphere

⇒ πr²h = n * 4/3πr³

=> πr²(8r) = n * (4/3)π * (r/2)³

=> 8πr³ = n * (4/3)π * (r³/8)

=> 8 = (4n/24)

=> n = 192/4

=> n = 48

Hence, the number of balls are 48.

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