# Cups A and B are cone shaped and have heights of #35 cm# and #23 cm# and openings with radii of #14 cm# and #9 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?

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Yes, cup A will overflow when the contents of cup B are poured into it. To find out how high cup A will be filled, you can calculate the volume of cup B's contents and compare it to the volume of cup A.

The volume of a cone can be calculated using the formula: ( V = \frac{1}{3} \pi r^2 h ), where ( r ) is the radius and ( h ) is the height.

First, calculate the volume of the contents of cup B using its dimensions. Then, compare this volume to the volume of cup A. If the volume of cup B's contents is greater than the remaining volume in cup A after pouring, cup A will overflow. Otherwise, cup A will be filled to the height of its remaining volume after pouring.

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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.

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.

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.

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- Cups A and B are cone shaped and have heights of #32 cm# and #27 cm# and openings with radii of #12 cm# and #12 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?
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