You have a full cylindrical glass of water that stands 8 inches tall and has a radius of 1.5 inches. If 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 your answer to the nearest hundredth.

The volume of a cylinder is [ (pi) (radius)² (height) ] .
The volume of the big glass is [ (pi) (2.5)² (12) ] = 75 pi cubic inches.
The volume of the small glass is [ (pi) (1.5)² (8) ] = 18 pi cubic inches.
When you empty the small glass into the large one, the large one still has room for [ (75 pi cubic inches) minus (18 pi cubic inches) ] more water.
(75 - 18) (pi) cubic inches = 57 pi cubic inches = 179.07 cubic inches
(about 99.22 fluid ounces)

Answered by AL2006 | 2024-06-10

The volume of the smaller glass is 18π cubic inches, while the larger glass has a volume of 75π cubic inches. The difference in their volumes, which tells us how much more the larger glass can hold, is 57π cubic inches, approximately 179.07 cubic inches. Thus, the larger glass can hold about 179.07 cubic inches more water than the smaller glass.
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Answered by AL2006 | 2024-10-22