Cups A and B are cone shaped and have heights of #33 cm# and #23 cm# and openings with radii of #14 cm# and #7 cm#, respectively. If cup B is full and its contents are poured into cup A, will cup A overflow? If not how high will cup A be filled?

Answer 1

Cup A will be filled to a height of #5.75cm#

Volume of Cup B #v=pir^2h# #=pi(7)^2times23# #v=1127pi#

Volume of Cup A #v=pir^2h# #=pi(14)^2times33# #v=6468pi#

Therefore, Cup A will not overflow if the volume of Cup B is poured into A

To find the height reached in Cup A, we can use what we already know --> #r=14# and #v=1127pi# #v=pir^2h# #1127pi=pi(14)^2h# #1127=196h# #h=1127/196# #h=5.75cm#

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Answer 2

Violet Aldrich

Cup A will not overflow. Cup A will be filled to a height of 13 cm.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.