Question

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

Answer 1

Ratio in the radius and height of a cone =5:12 Volume=2512 $c{m}^3$

Let radius (r)=5x

Then height (h)=12x

$\therefore Volume=\frac{1}{3}\pi r^{2}h\Rightarrow \frac{1}{3}\times 3.14\times (5x{)}^2\times 12x=2512\Rightarrow 3.14\times 25x^2\times 12x=2512\times 312\times 25x^3=\frac{2512\times 3}{3.14}=x^3=\frac{2512\times 3}{12\times 25\times 3.14}=\frac{2512\times 3\times 100}{12\times 25\times 314}=8x^3=8=(2{)}^3\therefore x=2\therefore Radius\left(r\right)=5x=5\times 2=10cmandheight\left(h\right)=12x=12\times 2=24cmNowslantheight=\sqrt{r^2+h^2}=\sqrt{(10{)}^2+(24{)}^2}=\sqrt{100+576}=\sqrt{676}=26cm$

Hence, slant height =26 cm and radius=10 cm.