SOLUTION: A large cylindrical container with a height of 32 cm and a radius of 8 cm has water in it to a depth of 26 cm. A smaller cylindrical container with no water in it has a height of 2

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Question 1149397: A large cylindrical container with a height of 32 cm and a radius of 8 cm has water in it to a depth of 26 cm. A smaller cylindrical container with no water in it has a height of 28 cm and a radius of 5 cm. The smaller container is lowered into the larger. As it is lowered, water rises in the larger and then spills out onto the ground until the top of the smaller container is level with the top of the larger. As the smaller container is lowered further, water from the larger spills into the smaller. When the smaller container is lowered all the way, it is then removed. What is the difference, in cm, in the height of the water left in the larger container and the height of the water that spilled into the smaller?
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Volume of large cylinder: %28pi%29%288%5E2%29%2832%29+=+2048pi

Volume of water initially in large cylinder: %28pi%29%288%5E2%29%2826%29+=+1664pi

Volume of small cylinder: %28pi%29%285%5E2%29%2828%29+=+700pi

Amount of spillage when small cylinder is lowered into large cylinder: %281664pi%2B700pi%29-2048pi+=+316pi

Amount of water that flows into the small cylinder when it has been completely lowered into the large cylinder: %28pi%29%288%5E2%29%2832-28%29+=+256pi

Total volume of water initially in the large cylinder that is no longer in it after the small cylinder is removed: 316pi%2B256pi+=+572pi

Volume of water in large cylinder after small cylinder is removed: 1664pi-572pi+=1092pi

Height of water in large cylinder after small cylinder is removed: 1092pi%2F64pi+=+17.0625

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.

Word-in-word and number-in-number this problem was solved several months ago at the forum under this link

https://www.algebra.com/algebra/homework/Volume/Volume.faq.question.1129768.html

https://www.algebra.com/algebra/homework/Volume/Volume.faq.question.1129768.html