# Cups A and B are cone shaped and have heights of #25 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?

It will over flow

Both container have same base area but A has less height so less volume.

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No, cup A will not overflow. Cup A will be filled up to a height of ( \frac{{27 \times 12^2}}{{25 \times 12^2}} ) cm, which is approximately 11.808 cm.

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Yes, cup A will overflow. When cup B's contents are poured into cup A, the volume of cup B's contents exceeds the volume that cup A can hold without overflowing. Cup A will be filled to its capacity, which is determined by its volume, given by the formula:

[V = \frac{1}{3} \times \pi \times r^2 \times h]

where (r) is the radius and (h) is the height.

For cup A: [V_A = \frac{1}{3} \times \pi \times (12 , \text{cm})^2 \times 25 , \text{cm} = 12,600 \pi , \text{cm}^3]

For cup B: [V_B = \frac{1}{3} \times \pi \times (12 , \text{cm})^2 \times 27 , \text{cm} = 12,960 \pi , \text{cm}^3]

Since (V_B > V_A), when cup B's contents are poured into cup A, it will overflow.

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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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