Beer Glass Shapes
MaTHHH HeLPPPP?
Charly's Ice Cream is known for its root beer float. – The float is made by pouring more root beer 3 scoops of ice cream until the glass is full 0.5 inches from the top. – A glass in the form of a cylinder with a radius of 1.25 inches and a height of 8.5 inches. – Each scoop of ice cream is a sugar sphere has radius of 1.25 inches. * Will there be more ice or more root beer float? Explain your reasoning.
You are comparing volumes in this problem to first find the volume of an ice cream scoop. Volume of a sphere is 4/3Pir ^ 3 to the end and scoop of ice cream is 4/3Pi (1.25) ^ 3. Three scoops of ice cream so we will multiply that number by three. The total volume of ice cream: * 4/3Pi 3 (1.25) ^ 3 (about 24.5) is now the volume of root beer in the cup. This is a bit complicated. The volume of the cup can contain is Pi (1.25) ^ 2 * 8.5, but root beer only reaches to eight inches (8.5 to 0.5). If there were no ice cream in the cup, the volume of root beer would be Pi (1.25) ^ 2 * 8 (about 39) but not ice cream we have to subtract the volume of ice cream root beer possible volume. Thus Pi (1.25) ^ 2 * 8-3 * 4/3Pi (1.25) ^ 3 which is about 39 (root beer possible) – 24.5 (real ice cream volume = 14.5 (Origin of the volume of real beer) Since it is superior to 24.5 from 14.5, more ice cream in root beer float.
Beer Glass Holds 5 Beers