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

Question

asked Jan 5, 2020 140k views

1 Answer

Koloman · Answer 1 · 2020-01-12T02:22:59+0000

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
cubes are produced. Volume of a cube of side
is
s^(3) . The volume of a sphere of diameter
is
$(\pi d^(3))/(6)$ .

$(27\text{ cm})^(3)=n* ((\pi (4 cm)^(3))/(6) )\\\\19683\text{ cm}^(3)=n* (\frac{32\pi \text{ cm}^(3)}{3} )\\\\n=587.37$

n is rounded off to 587.

∴ 587 spherical pellets can be made.