Question

The measures of a solid cuboid are $66cm,42cm$ and $21cm$ respectively. How manyspheres with diameter $4.2cm$ each can be recasted by melting it.

Answer 1

Length (l) $=66cm$
Breadth (b) $=42cm$
and height $\left(h\right)=21cm$
Volume of cuboid $=l\times b\times h$
$=66\times 42\times 21{cm}^3$
Diameter of sphere recasted $=4.2cm$ radius $\left(r\right)=\frac{4.2}{2}=2.1cm$
Volume of sphere $=\frac{4}{3}\pi \times (2.1{)}^3$ Let by melting the cuboid n spheres are formed.
$\therefore$ Volume of cuboid $=n\times$ volume of sphere
$\Rightarrow 66\times 42\times 21=n\times \frac{4}{3}\times \frac{22}{7}\times (2.1{)}^3$
$n=\frac{66\times 42\times 21\times 3\times 7}{4\times 22\times 2.1\times 2.1\times 2.1}$
Hence, the number of sphere reformed $=1500$