Cups A and B are cone shaped and have heights of #33 cm# and #37 cm# and openings with radii of #12 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?
No, it will only be filled
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To determine if cup A will overflow when the contents of cup B are poured into it, we need to compare the volumes of the two cups.

Calculate the volume of cup A: Volume_A = (1/3)π(r_A)^2 * h_A

Calculate the volume of cup B: Volume_B = (1/3)π(r_B)^2 * h_B

Compare the volumes of cup A and cup B. If the volume of cup B is greater than or equal to the volume of cup A, cup A will not overflow when the contents of cup B are poured into it.

If cup A is not overflowed, calculate how high cup A will be filled by subtracting the initial volume of cup A from the total volume of cup B poured into it.

Calculate the remaining volume in cup A and use it to find the height the liquid reaches in cup A using the formula for the volume of a cone.
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When evaluating a onesided 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 onesided 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 onesided 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 onesided 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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