Question

The volume of a right circular cone is $4710cu.cm$. if the radius and height of the cone are in the ratio $3:4$, find its slant height, when $\pi =3\cdot 14$.

Answer 1

Given that

the volume of right circular

cone$=4710c.m^3$

and

radius:height$=3:4$

let radius$=r$

height$=h$

let the ratio$=x$

then

$h=4x$

$r=3x$

now,A.T.Q,

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

$4710=\frac{1}{3}\times 3.14\times (3x{)}^2\times 4x$

$4710\times 3=36x^3\times 3.14$

$x^3=125$

$x=5$

now,

radius$=3x=3\times 5=15cm.$

height$=4x=4\times 5=20cm.$

slant height(l)$=\sqrt{h^2+r^2}$

$=\sqrt{{20}^2+{15}^2}$

$\sqrt{400+225}$

$=\sqrt{6}25$

$=25c.m.$

then,

slant height(l)$=25c.m.$

Hence, this is the answer.