Question

Question 11
How many spherical lead shots each of diameter 4.2 cm can be obtained from a solid rectangular lead piece with dimensions 66 cm, 42 cm and 21 cm.

Answer 1

Given that , lots of spherical lead shots made from a solid rectangular lead piece.
Also, given that diameter of a spherical lead shot i.e sphere = 4.2 cm
$\therefore$ Radius of a spherical lead shot. $r=\frac{4.2}{2}=2.1cm[\because radius=\frac{1}{2}diameter]$
So, volume of a spherical lead shot . i.e sphere
$=\frac{4}{3}\pi r^3=\frac{4}{3}\times \frac{22}{7}\times (2.1{)}^3=\frac{4}{3}\times \frac{22}{7}\times 2.1\times 2.1\times 2.1=\frac{4\times 22\times 21\times 21\times 21}{3\times 7\times 1000}$
Now, length of rectangular lead piece., l= 66 cm
Breadth of rectangular lead piece = b = 42 cm
Height of rectangular lead piece i.e cuboid $=l\times b\times h=66\times 42\times 21$
From eq(1)

Number of spherical lead shots
$=\frac{Volumeofsolidrectangularleadpiece}{Volumeofasphericalleadshot}$
Number of spherical lead shots $=\frac{66\times 42\times 21}{4\times 22\times 21\times 21\times 21}=\frac{3\times 22\times 21\times 2\times 21\times 21\times 1000}{4\times 22\times 21\times 21\times 21}=3\times 2\times 250=6\times 250=1500$
Hence, the required number of spherical lead shots is 1500.