Glassware
Two glasses are given: one in the shape of a cone and the other in the shape of a hemisphere. Both have the same height and the same radius at their top.
Challenger
We pour 15 milliliters (ml) of syrup into the conical glass, which fills it to one-third of its height. How much water should we add to fill the glass completely? Express your answer in ml, rounded to the nearest whole number.
Mastermind
We fill the hemispherical glass with syrup to one-third of its height. We then add water to fill the glass completely, creating a nice glass of lemonade. To make a lemonade in the conical glass that is equally sweet to the lemonade in the hemisphere, up to what height should the cone be filled with syrup before topping it off with water? Express your answer as a percentage of the glass’s height, rounded to the nearest whole number.