Question

how many spherical pellets of diameter 4 cm can be made out of a cube of lead for which each edge measures 27 cm ? round the answer to the whole number

Answer 1

587

Step-by-step explanation:

       A lead cube of side $27\text{ cm}$ is used to make spherical pellets of diameter $4\text{ cm}$.

       As the volume of lead is conserved, the volume of raw material equals the volume of finished products.

       $\text{Volume of cube} = \text{Volume of spheres produced}$

Let us assume that $n$ cubes are produced. Volume of a cube of side $s$ is $s^{3}$. The volume of a sphere of diameter $d$ is $\dfrac{\pi d^{3}}{6}$.

       $(27\text{ cm})^{3}=n\times (\dfrac{\pi (4 cm)^{3}}{6} )\\\\19683\text{ cm}^{3}=n\times (\dfrac{32\pi \text{ cm}^{3}}{3} )\\\\n=587.37$

       n is rounded off to 587.

∴ 587 spherical pellets can be made.