Question

How many spherical lead shots each $4.2cm$ in diameter can be obtained from a rectangular solid of lead with dimensions $66cm,42cm,21cm$. $(Use\pi =\frac{22}{7})$

Answer 1

Let the number of lead shots be $x$

Volume of lead in the rectangular solid $=(66\times 42\times 21){cm}^3$

Radius of a lead shot $=\frac{4.2}{2}cm=2.1cm$

Volume of a spherical lead shot $=\frac{4}{3}\pi \times {\left(2.1\right)}^3{cm}^3$

Volume of $x$ spherical lead shots $=(\frac{4}{3}\times \frac{22}{7}\times {\left(2.1\right)}^3\times x){cm}^3$

Volume of $x$ spherical shots = Volume of lead in rectangular solid

$(\frac{4}{3}\times \frac{22}{7}\times {\left(2.1\right)}^3\times x)=66\times 42\times 21$

$\Rightarrow x=\frac{66\times 42\times 21\times 3\times 7}{4\times 22\times {\left(2.1\right)}^3}\Rightarrow x=1500$

$\therefore$ Number of lead shots$=1500$