Question

A solid metallic right circular cylinder $1.8$m high with diameter of its base $2$m is melted and recast into a right circular cone with base of diameter $3$m. Find the height of the cone.

Answer 1

Cylinder: $h=1.8m,d=2m\Rightarrow r=\frac{2}{2}=1m$
Cone: $d=3m,r=\frac{3}{2}=1.5m,h=?$
Volume of cylinder$=$Volume of cone $\therefore \pi r_{cy}^2{h}_{cy}=\frac{1}{3}\pi r_c^2{h}_c$
$\frac{22}{7}\times 1\times 1\times 1.8m^3=\frac{1}{3}\times \frac{22}{7}\times 1.5\times 1.5\times h_c{m}^3$
$\therefore h_c=\frac{\frac{22}{7}\times 1\times 1\times 1.8}{\frac{1}{3}\times \frac{22}{7}\times 1.5\times 1.5}=\frac{1.8\times 3}{1.5\times 1.5}=\frac{5.4}{2.25}=2.4$
$\therefore$ Height of the cone$=2.4$.