How many spherical bullets each of $5cm$ in diameter can be cast from a rectangular block of metal $11dm\times 1m\times 5dm$?

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How many spherical bullets each of $5cm$ in diameter can be cast from a rectangular block of metal $11dm\times 1m\times 5dm$ ?

How many spherical bullets each of $5cm$ in diameter can be cast from a rectangular block of metal $11dm\times 1m\times 5dm$ ?

It is given that,

A metallic block of dimension $11dm\times 1m\times 5dm$

The diameter of each bullet $=5cm$

As, we know that

Formula of volume of the sphere $=4\pi {{r}^{3}}$

As, we know that, $1dm={{10}^{-1}}m=0.1m$

The volume of the rectangular block $=1.1\times 1\times 0.5=0.55{{m}^{3}}$

Radius of the bullet $=5/2=2.5cm$

Assume the number of bullets made from the rectangular block be n.

Now from the question,

The volume of the rectangular block $=$ sum of the volumes of the n spherical bullets

$0.55=n\times 43\pi {{\left( 2.5 \right)}^{3}}$

Solving for n, we have

$n=8400$

Hence, $8400$ can be cast from the rectangular block of metal.

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