Question

Find the slant height of the cone, whose volume is $1232c{m}^3$ and height is $24cm$.

Answer 1

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

$h=24$ cm and $V=1232c{m}^3$ ..(given)

Thus,

$1232=\frac{1}{3}\pi \times r^2\times 24$

$\therefore r^2=\frac{1232\times 3}{\frac{22}{7}\times 24}=49$

$\therefore r=7$ cm.

Now, slant height of cone $\left(l\right)=\sqrt{r^2+h^2}$

$=\sqrt{7^2+{24}^2}=\sqrt{625}$

$=25$ cm.