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Cups A and B are cone shaped and have heights of #27 cm# and #24 cm# and openings with radii of #7 cm# and #14 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

Savannah Aguilar

Since volume of contents in cup A #(1385.44)# c.cm is less than that of cup B #(4926.02)# c.cm , cup A will overflow.

Height and radius of cup A is #h_a=27# cm ,# r_a=7# cm

Volume of cone is #1/3*pi*r^2*h :.V_a=1/3*pi*7^2*27# or

#V_a ~~ 1385.44# cubic cm.

Height and radius of cup B is #h_b=24# cm,# r_b=14# cm

# :.V_b=1/3*pi*14^2*24 or V_b ~~ 4926.02# cubic cm.

Since #V_a < V_b # , the content will overflow. [Ans]

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Answer 2

Maverick Smith

No, cup A will not overflow. Cup A will be filled to a height of approximately ( \frac{24}{27} ) of its total height, which is approximately ( \frac{24}{27} \times 27 ) cm, or 24 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.