Question

Find the curved surface area of a cone whose volume and height are $120\pi c{m}^3$ and $10cm$ respectively.

Answer 1

Let r,l,h be radius ,slant height and height

of cone .volume =$\frac{1}{3}\pi r^{2}h,C.S.A=\pi rl$

Given,$\frac{1}{3}\pi r^{2}h=120\pi \Rightarrow r^2=\frac{120\times 3}{10}=36\Rightarrow r=6$

Now ,in a cone ,$l^2=r^2+h^2=36+100=136$

$\Rightarrow l=\sqrt{136}=2\sqrt{34}cm$

$C.S.A=\pi rl=6\pi x2\sqrt{34}=12\pi \sqrt{34}c{m}^2$