the question of my book said:
a right circular conical vessel with the semi-vertical angle of 45 degree is placed on a horizontal table with its apex upwards. water is poured into the vessel through a small hole in the apex, at a uniform rate of 12 m^3/s
........ another question said:
water is flowing at the rate of 10 cm^3/s into a leaking inverted circular cone of semi-vertical angle of 30 degree ............
what does that semi-vertical angle mean?
As usual, if I don't undferstand a term, I look it up in the internet.
Google gave me a website that says,
About the word 'vertical'
'Vertical' has come to mean 'upright', or the opposite of horizontal. But here, it has more to do with the word 'vertex'. Vertical angles are called that because they share a common vertex.
So the vertical angle of a right circular cone is the apex angle of its cross-section along the height.
Semi-vertical angle then is half of that vertical anglpe.
In your posted drawings, the one defined at the cone to the right is the semi-vertical angle.
So, a semi-vertical angle of 45 degrees has 2(45) = 90 degrees for its full vertical angle.