Question

A solid right circular cylinder of radius 60 cm and height 20 cm is melted and recast into a right circular cone of height 3 times that of the cylinder. Find the curved surface area of the cone in square cm correct up to two places of decimal. $(Use\pi =3.14)$

Answer 1

For cylinder: radius $=Rcm$, height $=hcm$
For cone: radius $=rcm$, height $=Hcm$
According to question,
Volume of metal used for making cylinder and cone are equal.
$\therefore \pi R^{2}h=\frac{1}{3}\pi r^{2}H\Rightarrow (60{)}^2\times 20=\frac{1}{2}{r}^2\times 60\Rightarrow r=60cm$
$\therefore$ Slant height of cone, $l=\sqrt{r^2+H^2}=\sqrt{(60{)}^2+(60{)}^2}=\sqrt{7200}=60\sqrt{2}m$
$\therefore$ Curved surface area of cone $=\pi rl=3.14\times 60\times 6\sqrt{2}c{m}^2=15983.86c{m}^2$