Question

The radius and the height of a right circular cone are in the ratio 5:12.If its volume is 314 cubic metre,find the slant height and radius $(Use\pi =3.14)$

Answer 1

Ratio in the radius and height of a cone =5:12 Volume=314 $c{m}^3$

Let radius (r)=5x

and height (h)=12x

$\therefore Volume=\frac{1}{3}\pi r^{2}h\Rightarrow 314=\frac{1}{3}\times 3.14\times \left(5x{)}^2\right(12x)\Rightarrow 314\times 3=3.14(25x^2\times 12x)\Rightarrow \frac{314\times 3}{3.14}=300x^3\Rightarrow \frac{314\times 3\times 100}{314\times 300}=x^3\Rightarrow x^3=1=(1{)}^3\therefore x=1\therefore Radius\left(r\right)=5x=5\times 1=5mandheight\left(h\right)=12x=12\times 1=12mNowslantheight=\sqrt{r^2+h^2}=\sqrt{(5{)}^2+(12{)}^2}=\sqrt{25+144}=\sqrt{169}=13m$