how did we get V= pih^3 ???

Question

it's a very long question so i took a screenshot of it here 

 

http://s4.postimg.org/qyasoc7p9/image.jpg

 

i checked the marks scheme and i don't understand how do we get V=πh³ from V=¹/₃πr²h ????

 

i know how to do everything else correctly

Answer 1

If you draw a radius at the water line, you form a right triangle with legs r and h and hypotenuse is the edge of the cone. Using trigonometry we see tan 60 degrees = r/h = √3

 

Therefore r = √3 h

 

Starting with formula V = (1/3)πr²h = (1/3) π (√3 h)² h = (1/3)π 3h² h = πh³

 

So V = πh³