The half-height cone glass

Filled to half the height, what % of a full glass is the drink?

Drag the drink level up and down. Compare the height with the amount of drink.

Volume grows with height × width × depth. At half height the drink is a cone half as tall, half as wide and half as deep: ½ × ½ × ½ = 1/8 = 12.5%.

So how high must you fill the cone glass to get half the drink?

You need height³ = ½, so height = ∛0.5 ≈ 0.794. Fill to 79.4% of the height and you have exactly half the drink. Drag the level there to check.