Question

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.

• A. 1500
• B. 1900
• C. 1600
• D. 1200

Answer 1

The correct option is A 1500

Given that , spherical lead shots are made from a solid rectangular lead piece.
Also, given that diameter of a spherical lead shot = 4.2 cm
$\therefore$ Radius of a spherical lead shot,
$r=\frac{4.2}{2}=2.1cm[\because radius=\frac{1}{2}(diameter\left)\right]$
So, volume of a spherical lead shot
$=\frac{4}{3}\pi r^3=\frac{4}{3}\times \frac{22}{7}\times (2.1{)}^3=\frac{4}{3}\times \frac{22}{7}\times 2.1\times 2.1\times 2.1=(\frac{4\times 22\times 21\times 21\times 21}{3\times 7\times 1000})c{m}^3$

Given, length of rectangular lead piece, l= 66 cm
breadth of rectangular lead piece, b = 42 cm
Height of rectangular lead piece, h = 21 cm
Therefore, volume of the rectangular lead piece (i.e., a cuboid) $=l\times b\times h=(66\times 42\times 21)c{m}^3$

Volume of rectangular lead piece = Number of sperical lead shots x volume of a spherical lead shot
$\Rightarrow Numberofsphericalleadshots=\frac{Volumeofsolidrectangularleadpiece}{Volumeofasphericalleadshot}=\frac{66\times 42\times 21}{\left(\frac{4\times 22\times 21\times 21\times 21}{3\times 7\times 1000}\right)}=\frac{3\times 22\times 21\times 2\times 21\times 21\times 1000}{4\times 22\times 21\times 21\times 21}=3\times 2\times 250=3\times 500=1500$

Hence, the required number of spherical lead shots is 1500.