If you have a full cylindrical glass of water that stands 8 inches tall and has a radius of 1.5 inches, and you pour the water into a larger cylindrical glass that stands 12 inches tall and has a radius of 2.5 inches, how much more water would the larger glass be able to hold? Round to the nearest hundredth.
Answer (2)
The volume of a cylinder is (π) (radius)² (height)
Volume of the larger glass = π (2.5)² (12) = 75 π cubic inches
Volume of the smaller glass = π (1.5)² (8) = 18 π cubic inches
If the smaller one is full to the rim, and you empty it into the larger one, then the larger one can still hold
( 75π - 18π ) = 57π cubic inches = 179.07 cubic inches
Man, that's some glass . . . about 78% of a gallon !
The larger glass can hold approximately 179.07 cubic inches more water than the smaller glass after pouring all the water from the smaller glass into it. This is calculated by finding the volume differences using the formula for the volume of a cylinder. The larger glass has a greater capacity due to its larger height and radius.
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