Question

Question 12
How many spherical lead shots of diameter 4 cm can be made out of a solid cube of lead whose edge measures 44 cm

Answer 1

Given that , lots of spherical lead shots made out of a solid cube of lead.
Given that, diameter of a spherical lead shot. i.e sphere = 4 cm
$\Rightarrow$ Radius of a spherical lead shot $=\left(r\right)=\frac{4}{2}$
r = 2cm $[diameter=2\times radius]$
So, volume of a spherical lead shot i.e . sphere
$=\frac{4}{3}\pi r^3=\frac{4}{3}\times \frac{22}{7}\times (2{)}^3=\frac{4\times 22\times 8}{21}c{m}^3$
Now, since edge of a solid cube (a) = 44 cm
So, volume of a solid cube $=(a{)}^3=(44{)}^3=44\times 44\times 44c{m}^3$

Number of spherical lead shots
$=\frac{Volumeofsolidcubeoflead}{Volumeofasphericalleadshot}$

From eq (i)
Number of spherical lead shots
$=\frac{44\times 44\times 44\times 21}{4\times 22\times 8}$
$=11\times 21\times 11=121\times 21$
$=2541$
Hence, the required number of spherical lead shots is 2541.