Step-by-step explanation:
A lead cube of side [tex]27\text{ cm}[/tex] is used to make spherical pellets of diameter [tex]4\text{ cm}[/tex].
As the volume of lead is conserved, the volume of raw material equals the volume of finished products.
[tex]\text{Volume of cube} = \text{Volume of spheres produced}[/tex]
Let us assume that [tex]n[/tex] cubes are produced. Volume of a cube of side [tex]s[/tex] is [tex]s^{3}[/tex]. The volume of a sphere of diameter [tex]d[/tex] is [tex]\dfrac{\pi d^{3}}{6}[/tex].
[tex](27\text{ cm})^{3}=n\times (\dfrac{\pi (4 cm)^{3}}{6} )\\\\19683\text{ cm}^{3}=n\times (\dfrac{32\pi \text{ cm}^{3}}{3} )\\\\n=587.37[/tex]
n is rounded off to 587.
∴ 587 spherical pellets can be made.
