If the surface area of the cone shown below is 628.32m2, find its volume.

Solution given:

diameter [d]=16m

radius [r]=8m

let slant height =l

surface area =628.32m²

πr(r+l)=628.32m²

π×8(8+l)=628.32

8+l=628.32/(8π)

8+l=25

l=25-8

l=17m

now

height of cone [h]=√{17²-8²}=15m

Again

Volume of cone =⅓πr²h=⅓×π×8²×15=320π 0r 1005.31m³

The required volume is 320π 0r 1005.31m³