Question

A right circular cone of radius 3 cm,has a curved surface area of 47.1cm^2,find the volume of cone.

Answer 1

Radius of the cone = 3cm

CSA of the cone = πrl sq.units

=> 47.1 sq.cm

Let us find slant height.

$47.1 = 3.14 \times 3 \times l$

$l = \frac{47.1}{3.14 \times 3}$

$l = 5 \: cm$

We know, radius and slant height, Let us find height.

$h = \sqrt{ {l}^{2} - {r}^{2} }$

$h \: = \sqrt{ {5}^{2} - {3}^{2} }$

$h = \sqrt{25 - 9 } = \sqrt{16} = 4 \: cm$

So, now Let us find the volume.

$volume = \frac{\pi {r}^{2} h}{3} \: cu.units$

$v = \frac{\pi \times {3}^{2} \times 4 }{3}$

$= 12\pi {cm}^{3} \: or \: 37.71 {cm}^{3}$

Hence the Answer