Question

The radius and the height of a right circular cone are in the ratio $5:12$ and its volume is $2512$ cubic cm. Find the radius and slant height of the cone. ($Take\pi =3.14$) ?

Answer 1

Let radius=5$x$ and height=12$x$

Volume of cone=$\frac{1}{3}\pi r^{2}h$

$2512=\frac{1}{3}\ast 3.14\ast 5x\ast 5x\ast 12x$

$\frac{2512\ast 3}{3.14}=300x^3$

$300x^3=2400$

$x^3=\frac{2400}{300}=8$

$x=2$

Radius=$5\ast 2=10cm$

Height=$12\ast 2=24cm$

$l=\sqrt{r^2+h^2}$

$=\sqrt{{10}^2+{24}^2}$

$=\sqrt{100+576}$

$=\sqrt{676}$

$=26$ cm