Question

A metalic cuboid 18cm *11cm*4cm is melted and recast into a core of radius 6cm.find the height of the cone

Answer 1

The volume melted = The volume recasted

Volume of cuboid = Volume of cone

$\textbf{lbh}$ = ${1/3}$ $\times{\pi r^2h}}$

$18 \times 11 \times 4$ = ${\frac{1}{3}}$
$\times{22/7\times{(6^2)h}}$

792 = ${\frac{1}{3}\times{22/7 \times{36h}}}$

$\frac{792 \times 7 \times 3}{22 \times 36} = h$

$\cancel{3}\:and\: \bcancel{36}$

$\frac{792 \times 7}{22 \times 12} = h$

$\cancel{792}\:and\:\bcancel{12}$

$\frac{66 \times 7}{22} = h$

$\cancel{66}\:and\: \bcancel{22}$

${3 \times 7} = h$

h = 21